Structured Finance The Object Oriented Approach Umberto Cherubini

Structured Finance The Object Oriented Approach Umberto Cherubini
Structured Finance The Object Oriented Approach Umberto Cherubini
Structured Finance The Object Oriented Approach Umberto Cherubini

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6. Structured Finance
The Object-Oriented Approach
Umberto Cherubini
Giovanni Della Lunga

8. Structured Finance

9. For other titles in the Wiley Finance Series
please see www.wiley.com/finance

10. Structured Finance
The Object-Oriented Approach
Umberto Cherubini
Giovanni Della Lunga

11. Copyright © 2007 John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester,
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Library of Congress Cataloging in Publication Data
Cherubini, Umberto.
Structured finance : the object oriented approach / Umberto Cherubini, Giovanni Della Lunga.
p. cm. — (Wiley finance series)
Includes bibliographical references and index.
ISBN 978-0-470-02638-0 (cloth : alk. paper) 1. Structured notes (Securities
3. Investment analysis—Mathematical models. 4. Financial engineering. I. Della Lunga, Giovanni.
II. Title.
HG4651.5.C46 2007
332.63

27—dc22
2007010265
British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library
ISBN 978-0-470-02638-0 (HB
Typeset in 10/12pt Times by Integra Software Services Pvt. Ltd, Pondicherry, India
Printed and bound in Great Britain by Antony Rowe Ltd, Chippenham, Wiltshire
This book is printed on acid-free paper responsibly manufactured from sustainable forestry
in which at least two trees are planted for each one used for paper production.

12. Contents
1 Structured Finance: A Primer 1
1.1 Introduction 1
1.2 Arbitrage-free valuation and replicating portfolios 2
1.3 Replicating portfolios for derivatives 3
1.3.1 Linear derivatives 3
1.3.2 Nonlinear derivatives 3
1.4 No-arbitrage and pricing 5
1.4.1 Univariate claims 5
1.4.2 Multivariate claims 7
1.5 The structuring process 8
1.5.1 The basic objects 9
1.5.2 Risk factors, moments and dimensions 9
1.5.3 Risk management 11
1.6 A tale of two bonds 13
1.6.1 Contingent coupons and repayment plans 13
1.6.2 Exposure to the risky asset 14
1.6.3 Exposure to volatility 14
1.6.4 Hedging 15
1.7 Structured finance and object-oriented programming 15
References and further reading 17
2 Object-Oriented Programming 19
2.1 Introduction 19
2.2 What is OOP (object-oriented programming)? 19
2.3 Analysis and design 20
2.3.1 A simple example 20
2.4 Modelling 25
2.4.1 The unified modelling language (UML
2.4.2 An object-oriented programming language: Java 26
2.5 Main ideas about OOP 27
2.5.1 Abstraction 27
2.5.2 Classes 28
2.5.3 Attributes and operations: the Encapsulation principle 28

13. vi Contents
2.5.4 Responsibilities 29
2.5.5 Inheritance 29
2.5.6 Abstract classes 34
2.5.7 Associations 34
2.5.8 Message exchanging 37
2.5.9 Collections 37
2.5.10 Polymorphism 37
References and further reading 42
3 Volatility and Correlation 45
3.1 Introduction 45
3.2 Volatility and correlation: models and measures 45
3.2.1 Implied information 47
3.2.2 Parametric models 47
3.2.3 Realized (cross
3.3 Implied probability 48
3.4 Volatility measures 50
3.4.1 Implied volatility 50
3.4.2 Parametric volatility models 51
3.4.3 Realized volatility 54
3.5 Implied correlation 55
3.5.1 Forex markets implied correlation 55
3.5.2 Equity “average” implied correlation 56
3.5.3 Credit implied correlation 56
3.6 Historical correlation 57
3.6.1 Multivariate GARCH 57
3.6.2 Dynamic correlation model 58
3.7 Copula functions 59
3.7.1 Copula functions: the basics 59
3.7.2 Copula functions: examples 60
3.7.3 Copulas and survival copulas 61
3.7.4 Copula dualities 62
3.8 Conditional probabilities 63
3.9 Non-parametric measures 64
3.10 Tail dependence 65
3.11 Correlation asymmetry 66
3.11.1 Correlation asymmetry: finance 66
3.11.2 Correlation asymmetry: econometrics 68
3.12 Non-exchangeable copulas 68
3.13 Estimation issues 70
3.14 Lévy processes 71
References and further reading 72
4 Cash Flow Design 75
4.1 Introduction 75
4.2 Types of bonds 76
4.2.1 Floaters and reverse floaters 76

14. Contents vii
4.2.2 Convertible bonds 76
4.2.3 Equity-linked notes 76
4.2.4 Inflation-linked bonds 77
4.2.5 Asset-backed securities 77
4.3 Time and scheduler issues 78
4.3.1 Payment date conventions 78
4.3.2 Day count conventions and accrual factors 79
4.4 JScheduler 80
4.4.1 Date handling in Java 80
4.4.2 Data models 85
4.4.3 Design patterns 98
4.4.4 The factory method pattern 99
4.5 Cash flow generator design 99
4.5.1 UML’s activity diagram 100
4.5.2 An important guideline to the data model for
derivatives: FpML 103
4.5.3 UML’s sequence diagram 109
4.6 The cleg class 110
References and further reading 111
5 Convertible Bonds 113
5.1 Introduction 113
5.2 Object-oriented structuring process 113
5.2.1 Financial asset class 114
5.3 Contingent repayment plans 114
5.3.1 Payoff class 115
5.4 Convertible bonds 117
5.4.1 Exercise class 117
5.5 Reverse convertible bonds 121
5.6 Barriers 121
5.6.1 Contingent convertibles: Co.Cos 121
5.6.2 Contingent reverse convertibles 122
5.6.3 Introducing barriers in the Payoff class 123
5.6.4 Parisian options: a short description 123
5.7 Pricing issues 125
5.7.1 Valuation methods for barrier options: a primer 125
5.7.2 The strategy pattern 126
5.7.3 The option class 127
5.7.4 Option pricing: aLego-like approach 129
References and further reading 135
6 Equity-Linked Notes 137
6.1 Introduction 137
6.2 Single coupon products 137
6.2.1 Crash protection 138
6.2.2 Reducing funding cost 141
6.2.3 Callability/putability: compound options 142

15. viii Contents
6.3 Smoothing the payoff: Asian options 150
6.3.1 Price approximation by “moment matching” 151
6.3.2 Variable frequency sampling and seasoning process 152
6.4 Digital and cliquet notes 153
6.4.1 Digital notes 153
6.4.2 Cliquet notes 154
6.4.3 Forward start options 154
6.4.4 Reverse cliquet notes 155
6.5 Multivariate notes 156
6.5.1 The AND/OR rule 156
6.5.2 Altiplanos 157
6.5.3 Everest 158
6.5.4 Basket notes 160
6.6 Monte Carlo method 161
6.6.1 Major components of a Monte Carlo algorithm 161
6.6.2 Monte Carlo integration 162
6.6.3 Sampling from probability distribution functions 163
6.6.4 Error estimates 164
6.6.5 Variance reduction techniques 165
6.6.6 Pricing an Asian option with JMC program 169
References and further reading 175
7 Credit-Linked Notes 177
7.1 Introduction 177
7.2 Defaultable bonds as structured products 177
7.2.1 Expected loss 178
7.2.2 Credit spreads 178
7.3 Credit derivatives 179
7.3.1 Asset swap spread 180
7.3.2 Total rate of return swap 181
7.3.3 Credit default swap 182
7.3.4 The FpML representation of a CDS 184
7.3.5 Credit spread options 187
7.4 Credit-linked notes 187
7.5 Credit protection 188
7.6 Callable and putable bonds 190
7.7 Credit risk valuation 191
7.7.1 Structural models 191
7.7.2 Reduced form models 193
7.8 Market information on credit risk 196
7.8.1 Security-specific information: asset swap spreads 196
7.8.2 Obligor-specific information: equity and CDS 197
References and further reading 201
8 Basket Credit Derivatives and CDOs 203
8.1 Introduction 203
8.2 Basket credit derivatives 203

16. Contents ix
8.3 Pricing issues: models 204
8.3.1 Independent defaults 204
8.3.2 Dependent defaults: the Marshall–Olkin model 205
8.3.3 Dependent defaults: copula functions 207
8.3.4 Factor models: conditional independence 207
8.4 Pricing issues: algorithms 211
8.4.1 Monte Carlo simulation 211
8.4.2 The generating function method 212
8.5 Collateralized debt obligations 213
8.5.1 CDO: general structure of the deal 213
8.5.2 The art of tranching 215
8.5.3 The art of diversification 217
8.6 Standardized CDO contracts 219
8.6.1 CDX and i-Traxx 220
8.6.2 Implied correlation 221
8.6.3 “Delta hedged equity” blues 222
8.7 Simulation-based pricing of CDOs 224
8.7.1 The CABS (asset-backed security) class 225
8.7.2 Default time generator 227
8.7.3 The waterfall scheme 228
References and further reading 230
9 Risk Management 233
9.1 Introduction 233
9.2 OTC versus futures style derivatives 234
9.3 Value-at-risk & Co. 235
9.3.1 Market risk exposure mapping 236
9.3.2 The distribution of profits and losses 237
9.3.3 Risk measures 238
9.4 Historical simulation 239
9.4.1 Filtered historical simulation 240
9.4.2 A multivariate extension: a GARCH+DCC filter 241
9.4.3 Copula filters 242
9.5 Stress testing 242
9.5.1 Sources of information 243
9.5.2 Consistent scenarios 243
9.5.3 Murphy’s machines 246
9.6 Counterparty risk 247
9.6.1 Effects of counterparty risk 247
9.6.2 Dependence problems 253
9.6.3 Risk mitigating agreements 254
9.6.4 Execution risk and FpML 258
References and further reading 259
Appendix A Eclipse 261
Appendix B XML 265
Index 283

18. 1
Structured Finance: A Primer
1.1 INTRODUCTION
In this chapter we introduce the main, and first, concepts that one has to grasp in order to
build, evaluate, purchase and sell financial structured products. Structured finance denotes
the art (and science) of designing financial products to satisfy the different needs of investors
and borrowers as closely as possible. In this sense, it represents a specific technique and
operation of the financial intermediation business. In fact, the traditional banking activity,
i.e. designing loans to provide firms with funds and deposits to attract funds from retail
investors, along with managing the risk of a gap in their payoffs, was nothing but the most
primitive example of a structuring process. Nowadays, the structured finance term has been
provided with a more specialized meaning, i.e. that of a set of products involving the presence
of derivatives, but most of the basic concepts of the old-fashioned intermediation business
carry over to this new paradigm. Building on this basic picture, we will make it more and
more involved, in this chapter and throughout the book, adding to these basic demands and
needs the questions that professionals in the modern structured finance business address to
make the products more and more attractive to investors and borrowers.
The very reason of existence of the structured finance market, as it is conceived today,
rests on the same arguments as the old-fashioned banking business. That was motivated
as the only way for investors to provide funds to borrowers, just in the same way as any
sophisticated structured finance product is nowadays constructed to enable someone to do
something that could not be done in any other way (or in a cheaper way) under the regulation.
In this sense, massive use of derivatives and financial engineering appears as the most natural
development of the old intermediation business.
To explain, take the simplest financial product you may imagine, a zero coupon bond, i.e.
a product paying interest and principal in a single shot at the end of the investment. The
investor’s question is obviously whether it is worth giving up some consumption today for
some more at the end of the investment, given the risk that may be involved. The borrower’s
question is whether it is worth using this instrument as an effective funding solution for
his projects. What if the return is too low for the investors or so high that the borrower
cannot afford it? That leads straight to the questions typically addressed by the structurer:
what’s wrong with that structure? Maybe the maturity is too long, so what about designing a
different coupon structure? Or maybe investors would prefer a higher expected return, even
at the cost of higher risk, so why not make the investment contingent on some risky asset,
perhaps the payoff of the project itself? If the borrower finds the promised return too high,
what about making the project less risky by asking investors to provide some protection?
All of these questions would lead to the definition of a “structure” for the bond as close as
possible to those needs, and this structure will probably be much more sophisticated than
any traditional banking product.

19. 2 Structured Finance
The production process of a structured finance tool involves individuation of a business
idea and the design of the product, the determination and analysis of pricing, and the defini-
tion of risk measurement and management procedures. Going back again to the commercial
banking example, the basic principles were already there: design of attractive investment and
funding products, determination of interest rates consistent with the market, management of
the misalignment between asset and liabilities (or asset liability management, ALM). Mostly
the same principles apply to modern structured finance products: how should we assemble
derivatives and standard products together, how should we price them and manage risk?
The hard part of the job would then be to explain the structure, as effectively as possible,
to the investors and borrowers involved, and convince them that it is made up to satisfy their
own needs. The difficulty of this task is something we are going to share in this book. What
are you actually selling or buying? What are the risks? Could you do any better? We will see
that asking the right questions will lead to an answer that will be found to be straightforward,
almost self-evident: why did not I get it before? It is thereplicating portfolio. The bad and
good news is that many structured products have their own replicating portfolios, peculiar
to them and different from those of any other. Bad news because this makes the design of a
taxonomy of these products an impossible task; good news because the analysis of any new
product is as surprising and thrilling as a police story.
1.2 ARBITRAGE-FREE VALUATION AND REPLICATING
PORTFOLIOS
All of the actors involved in the production process described above, i.e. the structurer, the
pricer and the risk manager, share the same working tools: arbitrage-free valuation and the
identification of replicating strategies for every product. Each and every product has to be
associated to a replicating portfolio, or a dynamic strategy, well suited to deliver the same
payoff at some future date, and its value has to be equal to that of its replicating portfolio.
The argument goes that, if it were not so, unbounded arbitrage profits could be earned by
going long in the cheaper portfolio and going short in the dearer one. This concept is the
common fabric of work for structurers, pricers and risk managers. The structurer assembles
securities in a replicating portfolio to design the product, the pricer evaluates the products
as the sum of the prices of the securities in the replicating portfolio, and the risk manager
uses the replicating portfolio to identify the risk factors involved and make the appropriate
hedging decisions. Here we will elaborate on this subject to provide a bird’s-eye review of
the most basic concepts in finance, developed along the replicating portfolio idea. This would
require the reader to be well acquainted with them. For intermediate readers, mandatory
references for a broad introduction to finance are reported at the end of the chapter.
Under a standard finance textbook model the production process of a structured product
would be actually deterministic. In fact, the basic assumption is that each product is endowed
with an “exact” replicating strategy (the payoff of each product is “attainable”): this is what
we call the “market completeness” hypothesis. Everybody knows that this assumption is miles
away from reality. Markets are inherently “incomplete”, meaning that no “exact” replicating
portfolio exists for many products, and it is particularly so for the complex products in
the structured finance business. Actually, market incompleteness makes life particularly
difficult in structured finance. In fact, the natural effect is that the production process of
these securities involves a set of decisions over stochastic outcomes. The structurer would

20. Structured Finance: A Primer 3
compare the product being constructed against the cheapest alternative directly available
to the customers on the market. The pricer has to select the “closest” replicating portfolio
to come up with a reasonable price from both the buyer’s and the seller’s point of view.
Finally, the risk manager has to face the problem of the “hedging error” he would bear under
alternative hedging strategies.
1.3 REPLICATING PORTFOLIOS FOR DERIVATIVES
Broadly speaking, designing a structured product means defining a set of payments and
a set of rules determining each one of them. These rules define the derivative contracts
embedded in the product, and the no-arbitrage argument requires that the overall value of
the product has to be equal to the sum of the plain and the derivative part. But we may push
our replicating portfolio argument even further. In principle, a derivative may be considered
as a structure including a long or short position in a risk factor against debt or investment
in the risk-free asset. This is the standardleveragefeature that is the distinctive mark of a
derivative contract.
1.3.1 Linear derivatives
As the simplest example, take a forward contract CF(S,t;F(0T≡, that is the value at time
tof a contract, stipulated at time 0, for delivery at timeTof one unit of the underlyingSat
the priceF(0 Tis linear:S≥T≡–F(0
no-arbitrage argument, it is easy to check that the same payoff can be attained by buying
spot a unit of the underlying and issuing debt with maturityTand nominal valueF(0
No-arbitrage requires that the value of the contract has to be equal to that of the replicating
portfolio
CF≥S≤ t∼ F≥0≡≤ T≡=S≥t≡−v≥t≤ T≡F≥0≡ (1.1
wherev≥t,T≡is the discount factor function – that is, the value, at timet, of a unit of
currency to be due at timeT. By market convention, the delivery price is theforward price
observed at time 0, when the contract is originated. The forward price is technically defined
asF≥0≡≡S≥0≡/v≥0≤T≡, so that CF≥S≤0∼F≥0≡≤ T≡=0 and the value of the forward contract
is zero at origin. Notice that the price of a linear contract does not depend on the distribution
of the underlying asset. Furthermore, the replicating strategy does not call for a rebalancing
of the portfolio as time elapses and the value of the underlying asset changes: it is astatic
replicationstrategy.
1.3.2 Nonlinear derivatives
Nonlinear products, i.e. options, can be provided with a replicating portfolio by the same
line of reasoning. Take a European call contract, payoff max(S≥T≡–K, 0), with aKstrike
price for an exercise timeT. By the same argument, we look for a replicating portfolio
including a spot position in
cunits of the underlying and a debt position for a nominal
valueW
c. The price of the call option at timetis
CALL≥S≤ t∼ K≤ T≡=
cS≥t≡−v≥t≤ T≡W
c (1.2

21. 4 Structured Finance
Notice that replicating portfolio can be equivalently represented in terms of two other
elementary financial products. These two products are digital, meaning they yield a fixed
payoff is the event ofS≥T≡≥K, and 0 otherwise. The fixed payoff may be defined in terms
of units of the asset or in units of currency. In the former case the digital option is called
asset-or-nothing(AoN cash-or-nothing(CoN
that going long an AoN(S,t;K,T) for one unit of the underlying and going short CoN(S,t;
K,T) options forKunits of currency yields a payoff max(S≥T≡–K, 0). We then have (see
Figure 1.1)
CALL≥S≤ t∼ K≤ T≡=AoN≥S≤ t∼ K≤ T≡−KCoN≥S≤ t∼ K≤ T≡ (1.3
–1
1
3
5
7
9
11
13
15
5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 13 13.5 14 14.5 15
Underlying asset value at exercise time
CoN
Call
AoN
Call = AoN – Strike × CoN
Options Payoff
5
Figure 1.1Call option payoff decomposition in terms of digital options
Nonlinearity of the payoff implies that the value of the product depends on the probability
distribution ofS≥T≡. Without getting into the specification of such distribution, notice that
for scenarios under which the eventS≥T≡≥Khas measure 0 we have that both the AoN
and the CoN products have zero value. For scenarios under which the event has measure 1,
the AoN product will have a value ofS≥t≡and the CoN option (with payoff of one unit of
currency) will be worthv≥t,T≡. This amounts to stating that 0≤
c≤1 and 0≤W
c≤K.
Accordingly,
0≤CALL≥S≤ t∼ K≤ T≡≤CF≥S≤ t∼ K≤ T≡ (1.4
and the value of the call option has to be between zero and the value of a long position in
a forward contract. This is the most elementary example of an incomplete market problem.
Without further comment on the probability distribution ofS≥T≡, beyond the scenarios with
probability 0 and 1, all we can state are thepricing boundsof the product, and the corre-
sponding replicating portfolios that are technically called itssuper-replicating portfolios. The
choice of a specific price then calls for the specification of a particular stochastic dynamic
of the underlying asset and a correspondingdynamic replicationstrategy.

22. Structured Finance: A Primer 5
Once a specific price is obtained for the call option, the replicating portfolio of the
corresponding put option [payoff: max(K–S≥T≡, 0)] can be obtained from the well-known
put–call parityrelationship
CALL≥S≤ t∼ K≤ T≡−PUT≥S≤ t∼ K≤ T≡=CF≥S≤ t∼ K≤ T≡ (1.5
which can be immediately obtained by looking at the payoffs. Notice that by using the
replicating portfolios of the forward contract and the call option above, we have
CALL≥S≤ t∼ K≤ T≡−PUT≥S≤ t∼ K≤ T≡=≥⎡
c−1≡S≥t≡+v≥t≤ T≡≥K−W
c≡(1.6
Recalling the bounds for the delta and leverage of the call option, it is essential to check
that a put option amounts to a short position in the underlying asset and a long position in
the risk-free bond. The corresponding pricing bounds will then be zero and the value of a
short position in a forward contract.
1.4 NO-ARBITRAGE AND PRICING
Selecting a price within the pricing bound calls for the specification of the stochastic dynam-
ics of the underlying asset. A world famous choice is that of a geometric Brownian motion.
dS≥t≡=⎣S≥t≡dt+⎛S≥t≡dz≥t≡ (1.7
where dz≥t≡∼√≥0≤dt≡is defined a Wiener process and⎣and⎛are constant parameters
(driftanddiffusion, respectively). Technically speaking, the stochastic process is defined with
respect to a filtered probability space {≤⎡≤⎡
t≤P. The filtration determines the dynamics
of the information set in the economy, and the probability measurePdescribes its stochastic
dynamics. It is very easy to check that the transition probability ofSat any timeT>t,
conditional on the valueS≥t≡observed at timet, is log-normal. Assuming a constant volatility
⎛then amounts to assuming Gaussian log-returns.
1.4.1 Univariate claims
To understand how the no-arbitrage argument enters into the picture just remember that the
standardarbitrage pricing theory(APT
E
≡
dS≥t≡
S≥t≡
≥
=⎣dt=≥r+⎠⎛≡dt (1.8
whereris the instantaneous interest rate intensity andis themarket price of riskfor the
risk factor considered in the economy (the analysis can of course be easily extended to other
risk factors). The key point is that the market price of risk (for any source of risk) must be
the same across all the financial products. Financial products then differ from one another
only in their sensitivity to the risk factors. Based on this basic concept, one can use the
Girsanov theorem to derive
dS≥t≡=≥r+⎠⎛≡S≥t≡dt+⎛S≥t≡dz≥t≡=rS≥t≡dt+⎛S≥t≡dz
∗
≥t≡ (1.9

23. 6 Structured Finance
where dz
∗
≥t≡≡dz≥t≡+dtis a Wiener process in the probability space {≤⎡≤⎡
t≤Q. The
newQmeasure is such that any financial product or contract yields an instantaneous interest
rate intensity, without any risk premium. For this reason it is called therisk-adjustedmeasure.
To illustrate, consider the call option written onS, described above. We have
d CALL≥S≤ t∼ K≤ T≡=CALL≥S≤ t∼ K≤ T≡≥rdt+⎛
Calldz
∗
≥t≡≡ (1.10)
where⎛
Callis the instantaneous volatility that can be immediately obtained by Ito’s lemma.
Notice that Ito’s lemma also yields
E
Q≥d Call≡=
≡
Call
t
+
Call
S
rS≥t≡+
1
2

2
Call
S
2
⎛
2
S≥t≡
2
≥
dt=rCall dt (1.11
from which it is immediate to recover the Black–ScholesfundamentalPDE:
Call
t
+
Call
S
rS≥t≡+
1
2

2
Call
S
2
⎛
2
S≥t≡
2
−rCall=0 (1.12
Derivative products must solve the fundamental PDE in order to rule out arbitrage oppor-
tunities. The price of specific derivative products (in our case a European call) requires
specification of particular boundary solutions (in our case Call(T=max(S≥T≡–K, 0)).
Alternatively the solution may be recovered by computing an expected value under the
measureQ. Remember that under such a measure all the financial products yield a risk-free
instantaneous rate of return. Assume that in the economy there exists amoney market fund
B≥t≡yielding the instantaneous rate of returnr≥t≡:
dB≥t≡=rB≥t≡ (1.13
It is important to check that the special property of the measureQcan be represented as
a martingale property for the prices of assets computed using the money market fund as
thenumeraire:
E
Q
≤
S≥T≡
B≥T≡
∼
=
S≥t≡
B≥t≡
⇒E
Q
≤
CALL≥T≡
B≥T≡
∼
=
CALL≥t≡
B≥t≡
(1.14
For this reason, the measureQis also called anequivalent martingale measure(EMM
where the termequivalentrefers to the technical requirement that the two measures must
assign probability zero to the same events (complying with the super-replication bounds
described above).
An alternative way of stating the martingale property is to say that under measureQthe
expected value of each and every product at any future dateThas to be equal to its forward
price for delivery at timeT. So, for example, for our call option under examination we have
Call≥t≡=E
Q
≤
Call≥T≡
B≥t≡
B≥T≡
∼
=E
Q
⎡
⎣exp
⎛
⎝−
T

t
r≥u≡du
⎞
⎠max≥S≥T≡−K≤0≡
⎤
⎦
=v≥t≤ T≡E
Q⎦max≥S≥T≡−K≤0≡
(1.15

24. Structured Finance: A Primer 7
where we have assumedr≥t≡to be non-stochastic or independent on the underlying assetS≥t≡.
It is well known that the same result applies to cases in which this requirement is violated,
apart for a further change of measure from the EMM measureQto theforward martingale
measure(FMMQ(T≡: the latter is obtained by directly requiring the forward prices to be
martingales, using the risk-free discount bond maturing at timeT ≥v≥t≤ T≡) instead of the
money market fund as the numeraire.
Under the log-normal distribution assumption in the Black–Scholes model we recover a
specific solution for the call option price:
CALL≥S≤ t∼ K≤ T≡=
cS≥t≡−v≥t≤ T≡W
c (1.16
with

c= ≥d
1≡ W
c=K ≥d
2≡
d
1=
ln≥F≥t≡/K≡+⇒
2
/2≥T−t≡
⇒
√
T−t
d
2=d
1−⇒
√
T−t
F≥t≡≡
S≥t≡
v≥t≤ T≡
where (. F≥t≡is the forward price
ofS≥t≡for delivery at timeT.
While the standard Black and Scholes approach is based on the assumption of constant
volatility, there is vastly documented evidence thatvolatility, measured by whatever statistics,
is far from constant. Non-constant volatility gives rise to different implied volatilities for
different strikes (smile effect) and different exercise dates (term structure of volatility).
Option traders “ride” the volatility surface betting on changes in skewness and kurtosis
much in a same way as fixed income traders try to exploit changes in the interest rate term
structure. Allowing for volatility risk paves the way to the need to design a reliable model
for the stochastic dynamics of volatility. Unfortunately, no general consensus has as yet been
reached on such a model. Alternatively, one could say that asset returns are not normally
distributed, but the question of which other distribution could be a good candidate to replace
the log-normal distribution of prices (and the corresponding geometric Brownian motion)
has not yet found a definite satisfactory answer. This argument brings the concept ofmodel
riskas a paramount risk management issue for nonlinear derivative and structured products.
1.4.2 Multivariate claims
Evaluation problems are compounded in cases in which a derivative product is exposed to
more than one risk factor. Take, for example, a derivative contract whose underlying asset
is a functionf≥S
1≤S
2S
N≡. We may again assume a log-normal multivariate process for
each risk factorS
i:
dS
i≥t≡=∗
iS
i≥t≡dt+⇒
iS
i≥t≡dz
i≥t≡ (1.17
where we assume the shocks to be correlatedE≥dz
i≥t≡≤dz
j≥t≡≡=
ijdt. The correlation
structure among the risk factors then enters into the picture.

25. 8 Structured Finance
Parallel to the Black–Scholes model in a univariate world, constant volatilities and cor-
relations lead to the assumption of normality of returns in a multivariate setting. Extending
the analysis beyond the Black–Scholes framework calls for a different multivariate proba-
bility distribution for the returns. The problem is even more compounded because the joint
distribution must be such that the marginal distribution be consistent with the stochastic
volatility behaviour analysed for every single risk factor. A particular tool, which will be
used extensively throughout this book, enables us to break down the problem of identifying
a joint distribution into that of identifying the marginals and the dependence structure inde-
pendently. The methodology is known as thecopula functionapproach. A copula function
enables us to write
Pr≥S
1≤K
1≤S
2≤K
2S
n≤K
n≡=C≥Pr≥S
1≤K
1≡≤Pr≥S
2≤K
2≡Pr≥S
n≤K
n≡≡
(1.18
whereC≥u
1,u
2,,u
N≡is a function satisfying particular requirements.
Alternatively – particularly for derivatives with a limited number of underlying assets –
a possibility is to resort to the change of numeraire technique. This could apply to bivariate
claims, such as, for example, the option to exchange (OEX
right to exchange one unit of assetS
1againstKunits of assetS
2at timeT. The payoff is
then OEX≥T≡=max≥S
1≥T≡−KS
2≥T≡≤0≡. In this case, usingS
2as the numeraire, we may
use the Girsanov theorem to show that the prices of bothS
1andS
2, computed usingS
2≥T≡
as numeraire, are martingale. We then have
OEX≥t≡=S
2≥t≡E
M
≤
max
≡
S
1≥T≡
S
2≥T≡
−K≤0
≥∼
(1.19
withMa new martingale measure such thatE
M≥S
1≥T≡/S
2≥T≡≡=S
1≥t≡/S
2≥t≡. It is easy
to check that ifS
1andS
2are log-normal, it yields the famous Margrabe formula for
exchange options.
As a further special case, considerS
2≥t≡≡v≥t≤ T≡, that is, the discount factor function. As
we obviously havev≥T≤ T≡=1, we get
OEX≥t≡=v≥t≤ T≡E
M⎦max≥S
1≥T≡−K≤0≡ (1.20)
and measureMis nothing but theforward martingale measure(FMMQ≥T≡quoted above.
Furthermore, ifQ≥T≡is log-normal, we recover Black’s formula
CALL≥S≤ t∼ K≤ T≡=v≥t≤ T≡⎦⎡
cF≥S≤ t∼ T≡−W
c (1.21
where thedelta⎡
candleverageW
care defined as above.
1.5 THE STRUCTURING PROCESS
We are now in a position to provide a general view of the structuring process, with the
main choices to be made in the design phase and the issues involved for the pricing and
risk management functions. In a nutshell, the decision boils down to the selection of a set of
maturities. For each maturity one has then to design the exposure to the risk factors. Choices

26. Structured Finance: A Primer 9
are to be made concerning both the nature of the risk factors to be selected (interest rate risk,
equity, credit or others) and the specific kind of exposure (linear or nonlinear, long or short).
In other words, designing a structure product amounts to assembling derivative contracts to
design a specific payoff structure contingent on different realizations of selected risk factors.
1.5.1 The basic objects
Let us start with an abstract description of what structuring a financial product is all about.
It seems that it all boils down to the design of three objects. The first is a set of maturity
dates representing the due date of cash flow payments:
t
1t
2t
it
n
The second is a set of cash flows representing the interest payments on the capital
c
1c
2c
ic
n
The third is the repayment plan of the capital
k
1k
2k
ik
n
or (the same concept stated in a different way) a residual debt plan
w
1w
2w
iw
n
Building up a structured finance product amounts to setting rules allowing univocal definition
of each one of these objects. Note that all the objects may in principle be deterministic or
stochastic. Repayment of capital may be decided deterministically at the beginning of the
contract, according to standard amortizing schedules on a predefined set of maturities, and
with a fixed coupon payment (as a percentage of residual debt): alternatively, a flat, and
again deterministic, payment schedule can be designed to be split into interest and capital
payments. Fixed rate bonds, such as the so-called bullet bonds, are the most standard and
widespread examples of such structures. It is, however, in the design of the rules for the
definition of stochastic payments that most of the creative nature of the structurer function
comes into play. Coupon payments may be made contingent on different risk factors, ranging
from interest rates to equity and credit indexes, and may be defined in different currencies.
The repayment plan may instead feature rules to enable us to postpone (extendible bonds)
or anticipate (retractable bonds) the repayment of capital, or to allow for the repayment to
be made in terms of other assets, rather than cash (convertible bonds). These choices may
be assigned to either the borrower or the lender, and may be made at one, or several dates:
notice that this feature also contributes towards making the choice of the set of payment
dates stochastic (early exercise feature). As one can glean directly from the jargon used,
structuring a product means that we introduce derivative contracts in the definition of the
coupon and the repayment plans.
1.5.2 Risk factors, moments and dimensions
The core of the structuring process consists of selecting the particular kind of risk exposure
characterizing the financial product. With respect to such exposure, a structurer addresses

27. 10 Structured Finance
three basic questions. Which are the technical features of the product, or, in other words,
which is the risk profile of the product? Is there some class of investors or borrowers that
may be interested in such risk profile; that is, which is the demand side for this product?
Finally, one should address the question whether investors and borrowers can achieve the
same risk profile in an alternative, cheaper way – that is, which are the main competitors of
the product?
In this book we are mainly concerned with the first question, i.e. that of the produc-
tion technology of the structuring process, which is of course a mandatory prerequisite to
addressing the other two, which instead are more related to the demand and supply schedules
of the structured finance market.
In the definition of the risk profile of the product one has to address three main questions:
•Which kind of risk factors?
•Which moments of risk factors?
•Which dimension of risk factors?
Which kind of risk factors?
One has to decide the very nature of the risk exposure provided in the product. Standard
examples are
•interest rates/term structure risk;
•equity risk;
•inflation risk/commodity risk;
•credit risk/country risk;
•foreign exchange risk.
Very often, or should we say always, a single product includes more than one risk factor.
For example, interest rate risk is always present in the very nature of the product to provide
exchange of funds at different times, and credit risk is almost always present as the issuer
of the product often is adefaultableentity. Foreign exchange risk enters whenever the risk
factor is referred to a different country with respect to that of the investor or borrower.
Of course, these kinds of risk are, so to speak, “built-in to” the product, and are, loosely
speaking, inherited from standard contractual specification of the product such as the issuer,
the currency in which payoffs and risk factors are denominated. Apart from this, of course,
some risk factor characterizes the very nature, or the dominant risk exposure of the product, so
that, for example, we denote one product equity linked and another one credit linked. More
recent products, known ashybrids, include two sources of risk as the main feature of the
product (such as forex and credit risk in the so-called “currency risk swap”).
Which moments of risk factors?
The second feature to address is the kind of sensitivity one wants to provide to the risk
factors. The usual distinction in this respect is betweenlinearandnonlinearproducts.
Allowing for linear sensitivity to the risk factor enables us to limit the effect to the first
moment. The inclusion of option-like features in the structure introduces a second dimension
into the picture: dependence onvolatility. In the post-Black and Scholes era,volatilityis far
from constant, and represents an important attribute of every risk factor. This means that

28. Structured Finance: A Primer 11
when evaluating a structured product that includes a nonlinear derivative, one should take
into account the possibility that the value of the product could be affected by a change in
volatility, even though the first moment of the risk factor stays unchanged.
Which dimension of risk factor?
Themodel riskproblem is severely compounded in structured products in which the risk
factor is made up of a “basket” of many individual risk factors. These products are the very
frontier of structured finance and are widespread both in the equity and the credit-linked
segments of the market. Using a basket rather than a single source of risk in a structured
product is motivated on the obvious ground of providingdiversificationto the product,
splitting the risk factor intosystematic(ormarket) andidiosyncratic(or specific) parts.
From standard finance textbooks we know that the amount of systematic risk in a product
is determined by the covariance, or by the correlation between each individual risk factor
and the market. But we should also note that, in that approach, volatilities and correlation
of asset returns are assumed constant, and this is again clearly at odds with the evidence in
financial market data. Correlation then is not constant, and the value of a financial product
may be affected by a change in correlation even though neither the value of the risk factor
nor its volatility has changed. Again, this paves the way to the need to devise a model for
correlation dynamics, a question that has not yet found a unique satisfactory answer.
1.5.3 Risk management
The development of a structured finance market has posed a relevant challenge to the financial
risk management practice and spurred the development of new risk measurement techniques.
The increasing weight of structured financial products has brought into the balance sheet
of the financial intermediaries – both those involved on the buy and the sell side – greater
exposure to contingent claims and derivative contracts. Most of these exposures were new
to the traditional financial intermediation business, not only for the nature of risk involved
(well far beyond term structure risk) but also for the nonlinearity or exotic nature of the
payoffs involved.
Optionality
The increased weight of nonlinear payoffs has raised the problem of accuracy of the paramet-
ric risk measurement techniques, in favour of simulation-based techniques. The development
of exotic products, in particular, has given risk managers a two-fold problem: on the one
hand, the need to analyse the pricing process in depth to unravel the risks nested in the
product; on the other hand, the need to resort to acceptable pricing approximations in closed
form, or at least light enough to be called in simulation routines as many times as necessary.
Nonlinear payoffs have also raised the problem of evaluating the sensitivity of the market
value of a position to changes in volatility and correlation, as well as the shape of the
probability distribution representing the pricing kernel.
Measurement risk
Coping with a specification of volatility and correlation immediately leads to other risks
that are brought into the picture. One kind of risk has to do with volatility and correlation

29. 12 Structured Finance
estimation. Thismeasurement riskproblem is common to every statistical application and
has to do with how a particular sample may be considered representative of the universe of
the events from a statistical inference point of view. Some technical methods can be used to
reduce such estimation risk. In financial applications, however, this problem is compounded
by the need to choose the proper information source – a choice that is more a matter of
art than science and calls for good operating knowledge of the market. What is typical of
financial applications is in fact the joint presence of “implied” and “historical” information
and the need to choose between them. So, what is the true volatility figure? Is it the implied
volatility backed out from a cross-section analysis of option prices, or is it to be estimated
from the time series of prices of the underlying assets? Or do both cross-section prices and
time series data include part of the information? And what about correlation?
Model risk
A different kind of risk has to do with the possible misspecification of the statistical model
used. Apart from the information source used and the technique applied, the shape of the
probability distribution we are using may not be the same as that generating the data. This
model risktakes us back to the discussion above on possible statistical specifications for
volatility and correlation dynamics in a post-Black and Scholes world. As we stated previ-
ously, no alternative model has been successful in replacing the Black–Scholes framework.
Apart from choosing a specific model, however, one can cope with model risk by asking
which is the sign of the position with respect to volatility and correlation and performing
stress testing analysisusing alternative scenarios.
Long-term risk
A particular feature of many structured finance products that compounds the problems of
bothmeasurementandmodelrisk is that typically the contingent claims involved are referred
to maturities that are very far in the future. It is not unusual to find embedded options to
be exercised in five years or more. The question is then: Which is a reasonable volatility
figure for the distribution of the underlying asset in five years? There is no easy way out
from thislong-term riskfeature, other than sticking to the standard Black–Scholes constant
volatility assumption, or sophisticated models to predict persistent changes in volatility.
Again, a robust solution is to resort to extreme scenarios for volatility and correlation.
Counterparty risk
Last, but not least, structured finance has brought to the centre of the scenecounterparty risk.
Not only do these products expose the investor and/or the borrower to the possibility that the
counterparty could not face its obligation, but very often these products arehedged, resorting
to aback-to-backstrategy on theover-the-counter(OTC
products, including complex exotic derivatives, that may be particularly difficult todelta–
gamma hedgeon organized markets. So, to take the example of a very common product, if
one is issuing an equity-linked note whose payoff is designed as a basket Asian option, he
can consider hedging the embedded option position directly on the market, or can hedge it
on the OTC market by buying an option with the same exact features from an investment
bank. The cost of the former choice is the need to have sophisticated human resources, and
some unavoidable degree ofbasis riskand/orhedging risk. The risk with the latter choice is

30. Structured Finance: A Primer 13
default of the counterparty selling the option, in which case one has to look for a different
counterparty and to pay a new premium to keep the position hedged (substitution cost).
Allowing for counterparty risk causes weird effects on the risk management of derivative
products. Not only is it dangerous to overlook this source of riskper se, but it may also
interfere with market risk inasmuch as counterparty risk is not taken into account in the
pricing and hedging activity.
1.6 A TALE OF TWO BONDS
In the spirit of introducing the reader to the methodology of structured products, rather
than to a classification, we now provide an example involving two of the easiest cases: an
equity-linked and a reverse convertible bond. While these products are probably very well
known even to non-professional readers, we think that following them in a sort of “parallel
slalom”, rather than one by one, would help to summarize and highlight some of the basic
methodological aspects discussed above, which are of general interest for the analysis of
any other product.
Take a zero coupon bond by which investors provide funding to some borrower. The
maturity of the zero coupon bond isTand the nominal amount of principal isL. Define
S≥T≡the value of a risky asset at the date of maturity of the bond.
Consider the two following structures:
•Equity-linked note: At timeTthe note will pay:
(i L;
(ii r
g(typically low and
unattractive) and the rate of appreciation of the risky asset with respect to a given
valueK: max≥r
g,S≥T≡/K−1≡.
•Reverse convertible note: At timeTthe note will pay:
(i Lif the value ofS≥T≡is greater than some valueK, and an amount of
stocks equal ton=L/Kotherwise: min≥L≤ n
S≥T≡
);
(ii r
g(typically pretty high and attractive).
We will now provide a comparative analysis of these two products, asking which are the
similarities and the differences.
1.6.1 Contingent coupons and repayment plans
At a glance, it is immediately clear that both products include nonlinearities, and option-like
derivatives. A first difference that emerges from mere description of the payoffs is that in
the equity-linked note case the nonlinearity is introduced in the coupon payment, while in
the reverse convertible case the derivative component is in the repayment plan.
We may be more precise and discover by straightforward manipulation that the coupon
rate of the equity-linked note is given by
Coupon=r
g+max

0≤S≥T≡−

1+r
g

K

/K (1.22

31. 14 Structured Finance
that is, a constant partplusthe payoff of a call option. The repayment of the principalLis
guaranteed.
In the reverse convertible the coupon payment is guaranteed while it is the repayment of
principal that is contingent on the risky assetS≥T≡. We have
Repayment=L−max⎦0≤L−nS≥T≡=L−nmax⎦0≤K−S≥T≡
=L−Lmax⎦0≤K−S≥T≡/K (1.23
and the principal repaid will consist of the principalminusthe payoff of a put option.
1.6.2 Exposure to the risky asset
The two products above include a part of the payoff contingent on the value of the risky
assetS. The question that immediately follows is their sensitivity to changes in the value of
that asset. Does the investor have a long or short position in the assetS? It may be surprising
to discover that from this point of view the two products are similar.
Let us start with the equity note. We saw that this product includes a long position in a
call option. It is well known that buying a call option is a way to take a long position on
the underlying asset for adelta(0≤⎡
c≤1) quantity funded by leverage (0≤W
c≤strike).
The value of the equity-linked note (ELN
ELN=v≥t≤ T≡

1+r
g

+
CALL

S≤ t∼

1+r
g

K≤ T

K
=v≥t≤ T≡

1+r
g

+⎡
c
S≥t≡
K
−v≥t≤ T≡
W
p
K
(1.24
On the contrary, we know that a put option represents a short position for adelta⎡
p=
⎡
c−1≥−1≤⎡
p≤1≡and a long position in the risk-free asset, such thatW
p=K−W
c.
Notice, however, that the reverse convertible note (RCN
option. AssumingL= 1 we then have
RCN=v≥t≤ T≡

1+r
g

−PUT≥S≤ t∼ K≤ T≡/K
=v≥t≤ T≡

1+r
g

+≥1−⎡
c≡
S≥t≡
K
−v≥t≤ T≡
K−W
c
K
(1.25
We may then check that both the equity-linked and the reverse convertible products share
the same feature of alongposition in therisky assetfunded by a leverage position.
1.6.3 Exposure to volatility
An increase in the value of the underlying asset would then have a positive effect on both of
the structured products. What about a change in volatility? Standard option pricing theory
suggests that response of the two products should now be opposite. The equity-linked note
in fact embeds a long position in an option, and, unless the option itself is endowed with
complex exotic features, that causes the value of the product to be positively affected by a
volatility increase. An increase in volatility would also increase the value of the put option
in the reverse convertible product, but as in this case the option is sold by the investor to the

32. Structured Finance: A Primer 15
issuer, that would subtract value from the product. So, recognizing a long or short position
in volatility is another question that any investor has to address. Notice that in this case –
where we have plain vanilla options – it coincides with being long or short in an option,
but that is not a general result. If, for example, as often happens in real world cases, barrier
option were used, the sign of exposure to volatility should be measured case by case.
1.6.4 Hedging
The difference between the two products also emerges, in quite a neat form, in a dynamic
hedging perspective. Consider a hedging policy in discrete time for both of the products.
In both cases, delta hedging would require us to take a short position in the underlying
asset. From standard option pricing theory we know that delta hedging is effective against
infinitely small changes of the underlying asset, but what about the impact of finite changes
in the underlying? This question may be relevant if the hedging portfolio is not frequently
rebalanced or the underlying moves a lot between the rebalance dates. It is easy to see
that this second-order effect, calledgammaexposure, has different sign in the two cases.
In the equity-linked note case changes of the underlying increase the value of the product,
while they correspondingly decrease the value of the reverse convertible note. It should be
remembered that as this is a second-order effect, the impact is due to the absolute change
in the underlying, rather than its direction: so, a delta-hedged investment position in a
reverse convertible note leaves the investor exposed to losses from finite changes of the
underlying no matter what their directions, and agamma-hedgingstrategy would be strongly
recommended.
1.7 STRUCTURED FINANCE AND OBJECT-ORIENTED
PROGRAMMING
As we saw above, the job of every participant in the structured finance business is to
assemble objects. Every product can be decomposed in a stream of cash flows and every
cash flow in a set of long and short positions. The term “object” introduces another function
that is particularly relevant in the structured finance team, and that is central in this book:
IT design and software engineering.
Object-Oriented Programming(OOP
based on the idea of partitioning the programming tasks in elementary units that are then
linked together to perform the overall task. The main advantage in favour of OOP is in
reusability of the code and updating. In case some adjustment is needed, one has to focus
only on the interested part without rewriting the entire code from scratch. Furthermore, the
objects are black boxes, including methods and attributes, that can be used without in-depth
knowledge of their content. So, when one takes an object called “option”, for example, he
would take something that would have some methods to compute prices, deltas, leverage,
and the like, without any need to know anything about the model used to compute them.
The software engineer and the financial engineer look at the concept of “object” with
different attitudes. For software engineers, an object is something in which to hide attributes
and methods; it is something toforget about. For financial engineers, an object is something
to unbundle in order to understand more about its working; it is something tolearn from.
But, curiously enough, in structured finance the objects are the same: they are the basic

33. 16 Structured Finance
components of the replicating portfolio. For this reason, both the software and financial
engineers very often find themselves designing a system of objects to represent and manage
structured products. The result must be consistent with the aims of both of them:
•It must carry the information content with respect to the risk factors as required by the
financial engineer.
•It must allow re-usability of code and code update as required by the software engineer.
Complying with the two targets is beneficial for the financial intermediary as a whole, and
the benefits are particularly relevant for the risk management process. A well-built object
oriented system
•would be able to speak out on the risks involved, the kind of risk, volatility and correlation;
•would allow a consistent update of prices and sensitivities of all the objects involved in
the structured products: changes of models are consistently “inherited” by all the products
in the portfolio;
•if the structure of the objects is finally shared with the counterparties, that could speed up
the transmission of information and could enable automated execution of the deal. This
source of execution risk is currently causing much concern to people in the market and
to the regulators.
The aim of this book is to reach both the financial engineer and the software engineer, and
to lay down a common set of tools for both of them. Our ambition is to make them meet
and work together sharing language and concepts. For this reason, we have attempted to
address every topic within the common language of the replicating portfolio, and the objects
involved, spelled out in the jargon of both the software engineer (OOP
engineer (building block approach). Every topic would be discussed in an object-oriented
framework, paying attention to: (i
(ii
XML language called FpML.
Chapter 2 introduces the main concepts of object-oriented programming, and the layout
of the basic language that the software engineer would share with the financial engineer.
The latter would in turn look for analogies between this language and that of the replicating
portfolio that is natural to him. Chapter 3 addresses the main concepts used by the financial
engineer to analyse the joint distribution of the risk factors, namely volatility and correlation,
both implied and historical.
Chapter 4 moves into the building of a structured financial product: here the software
engineer would disclose the problems involved in the construction of a schedule of payments,
and these arguments would be merged with the alternatives available to the structurer to
design a stream of cash flows (aleg, to borrow the wording from swaps) to meet the need
of a set of clients. Chapter 5 would address the use of derivative contracts to modify the
repayment plan of the product: these are mainly convertible andreverseconvertible bonds.
Chapter 6 will investigate in detail the construction of coupon plans indexed to equity
products, both univariate and multivariate. Chapter 7 will introduce credit-linked structured
products, limiting the analysis to univariate risks. Multivariate credit-linked products, which
represent the bulk of the structured finance market, will be addressed in Chapter 8.
Chapter 9 will finally address what is different about the structured finance business, as
far as risk management is concerned. In particular, historical filtered simulation and scenario

34. Structured Finance: A Primer 17
analysis techniques will be addressed in detail, as well as counterparty risk in derivatives,
which is one of the main reasons of concern in the finance world today.
REFERENCES AND FURTHER READING
Black, F. & Scholes, M. (1973 Journal of Political
Economy,81, 637–654.
Brigo, D. & Mercurio, F. (2006Interest Rate Models: Theory and Practice(2nd edition). Springer
Verlag, Berlin, Heidelberg, New York.
Cox, J.C. & Rubinstein, M. (1985Options Markets. Prentice-Hall, Englewood Cliffs, NJ.
Cox, J.C., Ingersoll, J.E. & Ross, S.A. (1985 Econo-
metrica,53, 385–407.
Cox, J.C., Ross, S.A. & Rubinstein, M. (1979 Journal of
Financial Economics,7, 229–263.
Dothan, M.U. (1990Prices in Financial Markets. Oxford University Press, New York.
Duffie, D. (2001Dynamic Asset Pricing Theory(3rd edition). Princeton University Press, Princeton.
Geman, H. (1989The importance of the forward risk neutral probability in a stochastic approach to
interest rates. Working Paper, ESSEC.
Harrison, J.M. & Kreps, D.M. (1979
Journal of Economic Theory,20, 381–408.
Harrison, J.M. & Pliska, S.R. (1981
trading,Stochastic Processes Applications,11, 215–260.
Harrison, J.M. & Pliska, S.R. (1983
markets,Stochastic Processes Applications,15, 313–316.
Heath, D.C., Jarrow, R.A. & Morton, A. (1990
A discrete time approximation,Journal of Financial and Quantitative Analysis,25, 419–440.
Heath, D.C., Jarrow, R.A. & Morton, A. (1992
A new methodology for contingent claim valuation,Econometrica,60, 77–105.
Hull, J. (2003Options, Futures and Other Derivatives. Prentice Hall, New Jersey.
Jamshidian, F. (1987Pricing of contingent claims in the one factor term structure model. Working
Paper, Merrill Lynch Capital Markets.
Jamshidian, F. (1997 Finance and Stochastics,1, 293–330.
Margrabe, W. (1978 Journal of Finance,33,
177–186.
Milne, F. (1995Finance Theory and Asset Pricing. Clarendon Press, Oxford.
Musiela, M. & Rutkowski, M. (2005Martingale Methods in Financial Modelling(2nd edition).
Springer Verlag, Berlin, Heidelberg, New York.
Ross, S.A. (1976 Journal of Economic Theory,13,
341–360.
Vasicek, O. (1977 Journal of Financial
Economics,5, 177–188.

36. 2
Object-Oriented Programming
2.1 INTRODUCTION
In this chapter we shall introduce the reader to the main ideas of Object-Oriented
Programming showing also some tools we can use for software design. It is important to
remember, however, that this is not a book about IT details or deep programming techniques,
so our main aim is to introduce the reader to a new way of thinking. Many good books are
available to those readers who want to go deeper into this fascinating subject.
We have decided to use, as a general programming environment, some tools that are
strongly based on the Java world but generally you should be able to read and understand
the arguments in this chapter even if you do not have a strong background in the Java
programming language.
What you should learn reading this chapter can be summarized as follows:
•The object-oriented way of thinking.
•The benefits of object-oriented software development.
•The basic concept of object orientation.
•Main ideas about UML and object-oriented analysis and design.
2.2 WHAT IS OOP (OBJECT-ORIENTED PROGRAMMING)?
Object-oriented programming (OOP for short) is a particular way of programming that
focuses on theresponsibilityof various tasks. The idea behind object-oriented programming
is that a computer program is composed of a collection of individual units, orobjects,as
opposed to a traditional view in which a program is a list of instructions to the computer.
Each object is capable of receiving messages, processing data, and sending messages to
other objects and should be responsible only for a particular task. To give you some idea of
what an object is, you can think of it as data and functionality packaged together in some
way to form a single unit of well-identified code (examples will be given below).
The peculiar feature of this approach is that special attention is given to creating the
appropriate objects as opposed to focusing solely on solving the problem. For this reason
OOP is often called aparadigmrather than a style or type of programming, to emphasize
that OOP can alter the way software is developed by changing the way programmers think
about it. A programming paradigm provides (and determines) the view the programmer has
of the execution of the program. On the one hand, for instance, in functional programming
a program can be thought of as a simple sequence of function evaluations. On the other
hand, in object-oriented programming programmers can think of a program as a collection
of interacting objects. Therefore the paradigm of OOP is essentially one of design and the
challenge in OOP is to design a well-defined object system.

37. 20 Structured Finance
OOP is particularly helpful in coping with complexity and building reusable computer
code. By breaking problems down into groups of smaller tasks performed by various objects,
complex problems can be managed and solved. This approach emphasizes code reusability,
which is extremely valuable to financial quants that are usually under time pressure. The
ability to cut and paste objects into new problems dramatically speeds up the development
process. This is a particularly important, probably the most important, point when we are
dealing with developing computational algorithms for structured finance. As a matter of
fact, as we have already introduced in Chapter 1, structurers, pricers and risk managers are
already accustomed to thinking in terms of objects because of the no-arbitrage/replicating
portfolio arguments.
2.3 ANALYSIS AND DESIGN
Any OOP problem-solving process can be broken down into three main categories: analysis,
design and implementation. Analysis refers to identifying the appropriate objects responsible
for the various tasks and the way they relate to each other: this exercise is often known as
data modelling. Once one has identified an object, it is generalized as aclassof objects (for
the time being just think of Plato’s concept of the “ideal” horse that stands for all horses)
and defined by the kind of data it contains. Any elaboration of data is performed by means
of functions calledmethods. Design refers to the structuring of the solution in terms of
appropriate classes. Finally, the design is converted into code in the implementation phase.
2.3.1 A simple example
The best way to explain the methodological approach we are talking about is to give a
practical example. We have seen that people in the structured finance market think of
financial products in terms of a collection of elementary objects. In a sense they think
in an objected-oriented way, even though they may not be aware of it. It is typically in
the interaction with a software engineer that they discover they are thinking in the OOP
approach: it is like a “maieutica” process that one can find in Plato’s classical dialogues. For
this reason the most effective way to get the ideas across is a dialogue between a software
architect (Giovanni
for structured finance: needless to say, every reference to facts, things or persons is purely
casual and involuntary. For the time being, the reader should not worry about understanding
every single detail of the conversation since each concept will be defined and described
more appropriately in the following paragraphs.
Giovanni:“Mate, you look puzzled, can I help you in any way?”
Umberto:“I am just thinking about this software for structured products. You know, the
only way you can define a structured product is as collections of other financial products.
It must be something similar to the concept of ‘object’ you IT guys are using, but I do not
know much more about that. Why don’t we try to fix ideas on a very simple product, say
a zero-coupon bond and an option? Let us focus on the representation of the option, you
know, they may be call or put, giving the right to buy or sell some underlying asset at a
certain price (strike or exercise price) at a certain date (exercise date).”
Giovanni: “Ok, we have an object which we call “option” and another one which is called
“underlying asset”. The underlying has the following properties: price, a real number,

38. Object-Oriented Programming 21
and volatility, a real number too. The attributes of an option are: a reference to its
underling asset and a flag to specify its payoff (call or put), the exercise price (strike
and the expiry date. Moreover, an option should also have a method in order to compute
its fair value. This method will be named “Pricing”. According to UML standard we can
describe our data in this way”
Umberto:“So, in general what describes an object? Could you explain this formalism in
more detail?”
Giovanni:“Option and Asset are two classes. A class is simply a prototype that defines the
variables and the methods common to all objects of a certain kind. As you can see in
this picture (Figure 2.1), the rectangles are divided into three sections: in the first one I
write only the name of the class; the second one contains the list of variables (for each
variable a data type and multiplicity are defined) which describe the behaviour of every
object of this type; finally in the last section we find the list of methods or operations.
The evaluation of an option, for example, is the result of a computational process that I
named ‘Pricing’. During the implementation of this class, the ‘Pricing’ method will be
designed in order to calculate the option price.”
Option
– Expiry : long [1]
– Payoff : int [1]
– Strike : double [1]
– Volatility : double [1]
– Price : double [1]
+ getVolatility : double
+ getPrice : double
+ setPrice : boolean
+ setVolatility : boolean
+ Pricing : double
+ setPayoff : boolean
+ setExpiry : boolean
+ setStrike : boolean
Asset
Figure 2.1Option and Asset classes
Class name
Attribute name
Attribute type
Multiplicity
Operations
– Volatility : double [1]
– Price : double [1]
+ getVolatility : double
+ getPrice : double
+ setPrice : boolean
+ setVolatility : boolean
Asset
Figure 2.2Notation elements for classes

39. 22 Structured Finance
Giovanni:“Now, we introduce the association between the two classes. This is simply a
relationship between different objects of the two classes; in our case the relationship is
due to the fact that each option has an underlying asset. We represent this association by
a single line between the classes, I’ll also write a name and a numerical specification,
which is called multiplicity, describing how many objects of one side of the association
are connected to how many object on the other side. For the time being we may stop to
consider univariate options, so this number is one.”
Option
– Expiry : long [1]
11has as underlying
– Payoff : int [1]
– Strike : double [1]
– Volatility : double [1]
– Price : double [1]
+ getVolatility : double
+ getPrice : double
+ setPrice : boolean
+ setVolatility : boolean
+ Pricing : double
+ setPayoff : boolean
+ setExpiry : boolean
+ setStrike : boolean
Asset
Figure 2.3Option and Asset classes with their relationship
Option
– Expiry : long [1]
11has as underlying
11country market is
Country
– Payoff : int [1]
– Strike : double [1]
– Volatility : double [1]
– Price : double [1]
– RiskFreeRate : double [1]
– Currency : String [1]
+ setCurrency : boolean
+ setRiskFreeRate : boolean
+ getRiskFreeRate : double
+ getCurrency : String
+ getVolatility : double
+ getPrice : double
+ setPrice : boolean
+ setVolatility : boolean
+ Pricing : double
+ setPayoff : boolean
+ setExpiry : boolean
+ setStrike : boolean
Asset
Figure 2.4Option, Asset and Country classes

40. Object-Oriented Programming 23
Umberto:“Uhmlet me thinkactually I may need more data in order to price an
option. I need to know the return volatility of the underlying and the risk-free interest rate
over the option life time.”
Giovanni:“You mean that the risk-free rate is not precisely a property of the option?”
Umberto:“No, I would say it is a feature of the particular currency area to which the option
belongs.”
Giovanni:“Wowfinally we have correctly structured data.”
Umberto:“For the particular application we are looking at, that is fine, but remember
that I want to use this class to price and simulate options.So, for example, I did
not mention that in some structured finance product we will encounter the so-called
‘early exercise feature’. Options may be European if they don’t allow early exercise or
Bermudan/American if they do so.”
Giovanni (just a bit angrier):“Ok, so we need to add another property which we
callExerciseTypethat can assume two different values, European and Early-
Exercise”
Umberto:“Uhm… of course you are surely aware that we must also allow for barriers, they
are present in many, many structured products”
Giovanni:“AAArghhhhh.”
Option
– Expiry : long [1]
11has as underlying
11country market is
Country
– Payoff : int [1]
– Strike : double [1]
– Exercise : Integer [1]
– Volatility : double [1]
– Price : double [1]
– RiskFreeRate : double [1]
– Currency : String [1]
+ setCurrency : boolean
+ setRiskFreeRate : boolean
+ getRiskFreeRate : double
+ getCurrency : String
+ getVolatility : double
+ getPrice : double
+ setPrice : boolean
+ setVolatility : boolean
+ Pricing : double
+ setPayoff : boolean
+ setExpiry : boolean
+ setStrike : boolean
+ setExercise : boolean
Asset
Figure 2.5The definitive (?

41. 24 Structured Finance
Introduction of barriers must be delayed to a later chapter because of a (hopefully
nervous breakdown of the software engineer. At this point of the process, however, we will
have a set of classes which, coded in (simplified
public class Asset {
public double getVolatility(
public double getPrice(
public boolean setPrice(double newPrice){}
public boolean setVolatility(double newVolatility){}
private double Volatility;
private double Price;
}
public class Country {
public boolean setCurrency(String newCurrency){}
public boolean setRiskFreeRate(double newRiskFreeRate){}
public double getRiskFreeRate(
public String getCurrency(
private double RiskFreeRate;
private String Currency;
}
public class Option {
public double Pricing(
public boolean setPayoff(Integer newPayoff){}
public boolean setExpiry(long newExpiry){}
public boolean setStrike(double newStrike){}
private long Expiry;
private int Payoff;
private double Strike;
private Asset lnkAttribute1;
private Country lnkAttribute2;
}
public class European_Option extends Option {
public double BlackScholes(
}
public class American_Option extends Option {
public double BinomialTree(
}
As we define different classes, we are digging deeper and deeper into the problem domain
of the business we are modelling. The more a system analyst interacts with the business he
is modelling, the more he discovers information belonging to different entities. This is how
the process works. We should not be afraid to create new classes. In the analysis phase we

42. Object-Oriented Programming 25
need not be concerned about it; the analysis phase is where we test ideas, new questions
and eventually evolve towards a solution that is sound, correct and shows the business as
it really is (or as we would like it to be). Let us not forget that design time is when it is
easiest to structure an application as a collection of self-contained modules or components
and this will in turn enable you to reuse code for different applications. Keep in mind that
this is the main task: when another application needs the same functionality, the designer
should quickly import it. Reusability and modularity of software code are two of the main
concepts of modelling, which we will begin to address in the next session.
2.4 MODELLING
In our case, with the word “modelling” we refer to the designing of software applications
before coding. Modelling is an essential part of large software projects, and is also helpful to
medium and even small projects. In software development, a model plays the analogous role
that blueprints and other plans (site maps, elevations, physical models) play in the building
of a skyscraper. Using a model, people responsible for a software development project can
make sure that business functionality is complete and correct, end-user needs are met, and
program design meets the requirements of scalability, robustness, security, extendibility and
other characteristics. All of this can be done before the implementation in code renders
changes difficult and expensive to make.
There are many different methods to describe the modelling process: one is by means of a
modelling language. The UML (Unified Modelling Language) is probably the most widely
used language, at least in the field of software engineering. In this book this language will
be used extensively, even though it will not be at a professional level, so we need to get at
least the flavour of this standard.
2.4.1 The Unified Modelling Language (UML
The Unified Modelling Language (UML
and design (OOAD
unifies the methods of Boock, Rumbaugh (OMT
that. The UML went through a standardization process with the OMG (Object Management
Group) and is now an OMG standard.
The UML is called a modelling language, not a method. Most methods consist, at least in
principle, of both a modelling language and a process. The modelling language is the (mainly
graphical) notation that methods use to express designs. In many ways the modelling language
is the most important part of the method and is certainly the key part for communication.
If you want to discuss your design with someone, it is the modelling language that both of
you need to understand, not the process you used to get to that design.
What can you model with UML? UML defines 12 types of diagram, divided into three
categories: four diagram types represent static application structures; five represent dif-
ferent aspects of dynamic behaviour; three represent ways you can organize and manage
your application modules. Structural Diagrams include the Class Diagram, Object Diagram,
Component Diagram, and Deployment Diagram. Behaviour Diagrams include the Use Case
Diagram (used by some methodologies during requirements gathering); Sequence Diagram,
Activity Diagram, Collaboration Diagram, and State Chart Diagram. Model Management
Diagrams include Packages, Subsystems and Models.

43. 26 Structured Finance
A deep understanding of UML constructions in all their varieties requires quite some
effort and is beyond the scope of this book. Our treatment will stick to the basic elements.
If the reader is interested in further technical details, he is advised to download the UML
specification from the OMG website (http://www.omg.org/uml/
is also highly technical, terse and very difficult for beginners to understand. In the following
sections we will use, and of course explain, the UML notation as we describe the main ideas
of object orientation.
2.4.2 An object-oriented programming language: Java
We have chosen Java as our reference language due to its extremely large diffusion and
to the availability of many free tools. As the reader probably already knows, Java is an
object-oriented programming language developed by Sun Microsystems in the early 1990s.
The main characteristic of Java is that, unlike conventional languages which are generally
either designed to be compiled to machine code (like C/C++ for example), or interpreted
from source code at runtime (like Microsoft Visual Basic for Application), Java is intended
to be compiled to a byte code which is then run by a Java virtual machine. Java is an
object-oriented language, this means that the language syntax (largely derived from C++)
all the various concept supports that we will find in this chapter. However, unlike C++,
which combines the syntax for structured, generic and object oriented programming, Java
was built from the ground up to be virtually fully object-oriented: everything in Java is an
object with the exceptions of atomic data types (ordinal and real numbers, boolean values,
and characters) and everything in Java is written inside a class.
Java Runtime Environment
The Java Runtime Environment (JRE
deployed on the Java Platform. End-users commonly use a JRE in software packages and
web browser plug-ins. Sun also distributes a superset of the JRE called the Java 2 SDK
(more commonly known as the JDK), which includes development tools such as the Java
compiler, Javadoc, and debugger.
Sun has defined three platforms targeting different application environments and seg-
mented many of its APIs so that they belong to one of the platforms. The platforms are:
•Java Platform, Micro Edition (Java ME) — targeting environments with limited resources,
•Java Platform, Standard Edition (Java SE) — targeting workstation environments, and
•Java Platform, Enterprise Edition (Java EE) — targeting large distributed enterprise or
Internet environments.
If you have not already installed a JRE on your computer you can find it at
http://java.sun.com/ (actually you can find here almost everything you need - at least for
Java beginners). For our needs the Standard Edition is required.
Components
One of the most important characteristics of Java is the enormous quantity of libraries
developed. Java libraries are compiled byte codes of source code developed by the JRE
implementer to support application development in Java. Many of these are becoming a
standard. Examples of these libraries are:

44. Object-Oriented Programming 27
•The core libraries, which include:
– Collection libraries which implement data structures such as lists, dictionaries, trees
and sets
– XML Parsing libraries.
•The integration libraries, which allow the application writer to communicate with external
systems.
•User Interface libraries, which include:
– The Abstract Windowing Toolkit (AWT
for laying out those components and the means for handling events from those com-
ponents
– The Swing libraries, which are built on AWT but provide (non-native
of AWT widgets.
We will not discuss further details about Java syntax and its architecture, but the reader is
referred to a very good tutorial material which can be found at
http://java.sun.com/docs/books/tutorial/index.html.
2.5 MAIN IDEAS ABOUT OOP
2.5.1 Abstraction
Object orientation is a method that represents things that are part of the real world as objects.
A computer is an object in the same way as a car or a financial asset. These objects are
in turn composed of other objects, and so on. Real-world objects can have a very complex
structure. Obviously in general we do not need to take into consideration every single details
of a real-world object; actually one of the main goals of the modelling process is to select
only essential aspects of the problem under consideration, neglecting useless information.
This particular process is called ‘Abstraction’.
Abstraction indicates the ability of a program to ignore some aspects of the information
that it is manipulating, i.e. the ability to focus on the essential. Abstraction is implicitly
present in everyday life. In a nutshell it means that we work with models of reality. One
of the authors is a railroad model fan and is used to playing with railroads, but not with a
real railroad of course (that will remain his unreachable dream). Engines, wagons, tracks,
crossings and buildings are scaled down representations of reality: it is a model railroad.
Software development does essentially the same: objects occurring in reality are reduced to
a few features that are relevant in the current situation.
Getting closer to our main application, an exact replicating portfolio for a structured
product or a derivative contract is something that emerges from a model of the market
in which many other features (e.g., transaction costs, institutional features, micro-structure
features, and so on) may bring about the final outcome. Instead of real objects we work with
symbols. It could happen that the same object, such as a financial option, could have different
representations in different projects. For example, let us think of two different applications,
the first oriented to pricing, the other to account management. It is very probable that the
two systems require different kind of information and this will be reflected directly on the
modelling of our options.

45. 28 Structured Finance
2.5.2 Classes
A class describes the structure and behaviour of a set of similar objects. An object is an
instance that is present at runtime, allocates memory for its instance variables and behaves
according to the protocol of its class.
In this book classes and objects are represented following the UML notation of rectangles
(see Figure 2.2). To differentiate between classes and objects, the names of the objects have
been underlined in the figure. If we want to represent the object–class relationship (instance
relationship), we draw a dashed arrow from an object in the direction of its class (Figure 2.6)
Class
Instance Of
Equity_Index
Object
S&P500
Figure 2.6Notation of class and object and an example of an instance relationship
2.5.3 Attributes and operations: the Encapsulation principle
The most important properties of a class areattributesandoperations(ormethods) which
are combined make up a single unit (the class itself). Attributes describe the structure of
the objects, their components and the information or data contained therein. Methods or
operations describe the behaviour of the objects. Attributes are only accessible indirectly via
the operations of the class.
Let’s get a closer look at the Java-like code produced for the Asset class
public class Asset {
// methods
public double getVolatility(
public double getPrice(
public boolean setPrice(double newPrice){}
public boolean setVolatility(double newVolatility){}
// attributes
private double Volatility;
private double Price;
}
As you can see, the wordprivateis written before the definition of attributes; this is called
a “modifier”. Another modifier in the class declaration ispublic. These modifiers affect the
way in which other objects can access attributes and method of our class. Since the modifier
of attributes isprivatethis means that no other object can access the data contained in

46. Object-Oriented Programming 29
these properties. The only way to get access to these values is by means of the methods
getVolatility( andgetPrice(which, on the other hand, are defined aspublic.
For readers who know just a bit of computer programming, this means that the attempt
to read/write data from/in our attributes directly with a code like
Asset myAsset
myAsset.Volatility = 9.8;
or
double price = myAsset.Price;
will produce an error condition. The correct instructions are instead
myAsset.setVolatility(9.8
double price = myAsset.getPrice(
The concept of hiding the inner structure of an object, and that the only way to access the
values is by means of well-defined methods, is often calledEncapsulationorHiding.
2.5.4 Responsibilities
Each class should be responsible for precisely one logical aspect of the total system. The
properties located in this area of responsibility should be grouped into a single class and
not divided over various classes. Moreover, a class should not contain properties that do
not belong to its area of responsibility. This is a very important principle in object-oriented
software development. Each responsibility is assigned to a single class. Each class is respon-
sible for one aspect of the total system. This, by the way, is a principle that has already been
implemented in previous programming paradigms. It is a sort of modularity requirement:
if you have, for example, a general program for computation of option pricing you should
design well-separated modules (or classes in our case) to handle data input, computation,
output and so on. In turn each of these classes should be divided into further subclasses to
handle single operations as elementary as possible.
2.5.5 Inheritance
Classes may represent specializations of other classes, i.e. classes can be arranged hier-
archically and assume (“inherit”
can specialize (“overwrite”
automatically have all properties of the superior class: thus, properties are inherited. This
principle is the cornerstone of reusability in the contest of OOP. The inheritance relation is
represented by an arrow with the subclass always pointing to the superclass. For example
it is possible to specialize the option class in order to manage the different exercise type
(Figure 2.7).
As we have already stated, in the generalization or specialization process of classes, a
subclass inherits the properties of its superclass, but it must also assume its responsibilities
and task, at least in principle. Particular features may be specialized – i.e. further developed –
and new features may be added. Existing properties, however, should be neither suppressed
nor restricted.

47. 30 Structured Finance
Figure 2.7Example of inheritance
But how are properties arranged inside an inheritance hierarchy? Fundamentally, properties
are situated precisely in those classes where, according to the responsibility assigned to
them, they are effectively a property of the class. Conversely classes contain precisely those
properties for which they are responsible. Consider, for example, the class COption and its
subclasses COption_European and COption_American (see Figure 2.7). A simplified Java
code is reported below (for the complete source code see the Java project Ch02_Example_01
on the CD enclosed).
// Class declaration
public class COption {
// Variables Declaration
protected double expiry;
protected double strike;
protected int payoff;
protected double asset_Price;
protected double asset_Volatility;
protected String country_Currency = "";
protected double country_RiskFreeRate;
// Class Constructor
public COption(
expiry = 0;
strike = 0;
payoff = -1;
asset_Price = -1;
asset_Volatility = -1;
country_Currency = ‘‘???’’;
country_RiskFreeRate = -1;
}

48. Object-Oriented Programming 31
// Methods
public double getExpiry(
return expiry;
}
public double getStrike(
return strike;
}
public int getPayoff(
return payoff;
}
public double getAsset_Price(
return asset_Price;
}
public double getAsset_Volatility(
return asset_Volatility;
}
public String getCountry_Currency(
return country_Currency;
}
public double getCountry_RiskFreeRate(
return country_RiskFreeRate;
}
public void setExpiry(double expiry) {
this.expiry = expiry;
}
public void setStrike(double strike) {
this.strike = strike;
}
public void setPayoff(int payoff) {
this.payoff = payoff;
}
public void setAsset_Price(double asset_Price) {
this.asset_Price = asset_Price;
}
public void setAsset_Volatility(double asset_Volatility) {
this.asset_Volatility = asset_Volatility;
}
public void setCountry_Currency(String country_Currency) {
this.country_Currency = country_Currency;
}
public void setCountry_RiskFreeRate(double country_
RiskFreeRate) { this.country_RiskFreeRate = country_
RiskFreeRate;
}
public Value(

49. 32 Structured Finance
{
return 0;
}
}
Theclass body(the area between the curly brackets) contains all the code that provides for
the life cycle of the objects created from the class.
TheCOptionclass declares seven instance variables:
•expirycontains the option expiration in years from evaluation date;
•strikecontains the option strike price;
•payoffan integer variable which identifies the type of option payoff (0 stand for a call,
1 for a put);
•asset_Priceandasset_Volatilitycontain the price and volatility of the under-
lying asset;
•country_Currencyis a string indicator for the currency;
•country_RiskFreeRate is a double variable that contains the risk-free spot rate
used for the option pricing.
The modifierprotected, written before each declaration, means that subclasses of
COptioncan access directly the value of these variables. Though this is not completely
accurate from the point of view of a pure object-oriented way of programming, this choice
allows us to write a less complicated code. Of course it is always possible to declare these
variables asprivateand use the appropriate methods to set and get their values.
TheCOptionclass also declares aconstructor– a subroutine used to initialize new
objects created from the class. You can recognize a constructor because it has the same
name as the class. TheCOptionconstructor initializes all seven of the object’s variables.
Some variables are set to-1, indicating that a generic objectCOptionis not usable when
the application starts up.
Finally the class declares 14 methods that provide ways for other objects to read and
change the value of instance variables without giving other objects access to the actual
variables (this is an application of the encapsulation principle mentioned in section 2.5.3)
and a methodValue(.
Let us now consider the two subclasses: COption_European and
COption_American.
// Class Declaration
public class COption_European extends COption
{
public double Value(
{
System.out.println("Pricing European Option...");
return 0;
}
public COption_European(double s,
double k,
double r,

50. Object-Oriented Programming 33
double t,
double sigma,
int type)
{
asset_Price = s;
asset_Volatility = sigma;
country_RiskFreeRate = r;
expiry = t;
strike = k;
payoff = type;
}
}
// Class Declaration
public class COption_American extends COption
{
public double Value(
{
System.out.println("Pricing American Option...");
return 0;
}
public COption_American(double s,
double k,
double r,
double t,
double sigma,
int type)
{
asset_Price = s;
asset_Volatility = sigma;
country_RiskFreeRate = r;
expiry = t;
strike = k;
payoff = type;
}
}
Since they are subclasses ofCOption, we do not need to define any variable, they simply
inherit every variable and every method from their superclass. Theextendsclause iden-
tifiesCOptionas the superclass of the class, thereby setting this class on top of the class
hierarchy. Since all the variables were defined asprotected, we can assign them directly
a new value in the constructor without calling the appropriate “get” methods. Notice that
constructors are not members and so are not inherited by subclasses.
An instance method in a subclass with the same signature and return type as an instance
method in a superclassoverridesthe superclass’s method; in our case the methodValue(

51. 34 Structured Finance
overrides the original method ofCOption. As we will see in the next section, a subclass
must always override methods that are declaredabstractin the superclass, or the subclass
itself must be abstract.
2.5.6 Abstract classes
Classes for which no concrete instances may be created, i.e. which will never become an
object, are calledabstract classes. In our example, there will be objects from the class
Option_European, or from the classOption_American, but none from theOption
class becauseOptionis merely an abstraction (there are no options without exercise
specification!). The class is only included in the model to sensibly abstract the (common
properties of the other classes.
Abstract classes are marked by the property valueabstractbelow the class name or by
the class name itself in italics. An abstract class can only be subclassed and cannot be
instantiated. To declare that your class is an abstract class, use the keywordabstract
before theclasskeyword in your class declaration:
abstract class COption
{
...
}
If you attempt to instantiate an abstract class, the compiler will display an error message. An
abstract class can containabstract methods– methods with no implementation. In this way,
an abstract class can define a complete programming interface for its subclasses, referring to
the subclasses for a complete and detailed implementation of those methods. As an example,
the classCOptiondeclares a methodValue(but the implementation of this method is
specialized in the subclasses since different valuation methods are required for European
and American options.
2.5.7 Associations
Anassociationis a relationship between different objects of one or more classes. A simple
example of association is the relationship between an option and its underlying asset.
Portfolio
– has_asset
Asset
1..*
Figure 2.8Example of an association
In the simplest case an association is represented by a single line between two classes.
Usually, however, associations are described in as much detail as possible. The association
receives a name and a numerical specification (multiplicity indication) of the number of
objects on one side of the association that are connected with a number of objects on the
other side. Furthermore, names are added which describe in more detail the meaning of the
class involved or their objects.

52. Object-Oriented Programming 35
A particular variation of association isaggregation. This is again a relationship between
two classes, but with the peculiarity that the classes relate to each other as a whole relates
to its parts. Aggregation is the composition of an object out of a set of parts. A portfolio,
for example, is an aggregation of assets. Aggregation is ahasrelationship (we say that a
portfoliohasdifferent assets).
A special form of aggregation is when the individual parts depend on the aggregate (the
whole) for their own existence: this is called acomposition. With composition any “part”
object may belong to only one “whole”; further, the parts are usually expected to live and
die with the whole. Usually any deletion of the whole is considered to cascade to the parts.
In an aggregation, the side of the whole is marked by a lozenge, to identify the relationship
as an aggregation. Associations are marked with white lozenges while composition are
marked by solid lozenges and have always a multiplicity of 1 (or 01) on the side of the
aggregate, i.e. where the lozenge is located.
The distinction between aggregation and composition is highly relevant for financial
applications, because it intervenes in the relationship between a financial product and its
replicating portfolio. Take the simplest example of a plain vanilla European option. We know
that its payoff is financially equivalent to a composite position in asset-or-nothing digital
and cash-or-nothing digital options. So, a way to synthetically construct an option would
be to take a suitable position in these digital options. The synthetically constructed option
would then be anaggregationof digital options: as a result, we could drop a part of the
replicating portfolio without closing down the entire position because there is no contractual
agreement linking the two obligations together. What about a plain, non-synthetic, option
contract? This is acompositionof digital options, meaning that the contracts in the replicating
portfolio disappear as soon as the option contract itself disappears; therefore, in this case,
the two obligations are wrapped together in the same contract. The IT representation then
makes a fine distinction between the two contracts, synthetic and non-synthetic, that we
often overlook in finance. This distinction, however, is of utmost practical relevance, as will
be discussed in detail in the chapter on counterparty risk. For the time being, we sketch out
the problem by a simple example.
Example 2.1Assume that you want to buy a call option on 10 000 Generali stocks for the
strike price of 20 euros, for three months from now. You can achieve the same result in two
different ways:
(a
strike of 20 and exercise in three months. According to the organization of the market,
the counterparty is going to be the clearing house of the Italian stock exchange (Cassa
di Compensazione e Garanzia, CCG).
(b
nothing option for a nominal value of 200 000 euros, with the same strike and exercise.
The products will be bought and sold on the over-the-counter (OTC
in a bilateral relationship.
Are the products and strategies (a
different. In the first case, default risk is very low and, if default occurs, all of the option
value will be lost. In the second case, default will only affect the asset-or-nothing option
that was bought from the counterparty. The difference between these two products of course
is expected to show up in a difference in price, and in the chapter on counterparty risk we
will see that this is actually the case.

53. 36 Structured Finance
In Figure 2.9 we have described a plain vanilla European option as acombinationof a
cash-or-nothing binary option and an asset-or-nothing binary option. From a general point of
view, aggregate objects can consist of objects of the same class. For example, let us consider
the aggregation depicted in Figure 2.9. The plain vanilla European option is described as an
aggregate object composed by two different options. However, it is very plausible that all
the three objects are subclasses of a superclass called COption, so the correct class diagram
should be that shown in Figure 2.10.
PVEuropeanOption
BinCoN_Option BinAoN_Option
has
Figure 2.9A simple example of aggregation
COption
PVEuropeanOption
has
has
BincoN_Option
BinAoN_Option
Figure 2.10Composite objects: combining inheritance and aggregation

54. Object-Oriented Programming 37
2.5.8 Message exchanging
Objects are independent units that cooperate and interact by means of messages they send to
each other. These messages lead to the operations, which means that an object may precisely
understand those messages for which it has operations. In contrast to conventional programs,
operations and data build a unit. An object contains all operations needed for processing
its data contents and all of its further behaviour. Facts that are related to each other by
their contents are concentrated inside the object. In an object-oriented solution, operations
or messages can only be accessed via the object:
object.message(arguments
For example, in order to evaluate the price of an option we have to call the methodValue(,
which is defined inside the classCOption
COption myOption;
myOption.Value(
Moreover, as has already been stated, object attributes are usually encapsulated and accessible
from outside only via appropriate operations (such asVolatilityof an asset which can
only be accessed via thesetVolatilityandgetVolatilityoperations).
2.5.9 Collections
Collection classes are usually defined in a standard class library and have in common that
they collect and manage sets of objects. Collections are also called container classes. They
have all the operations for adding and removing objects, checking whether a given object is
contained in the set and determining how many objects are currently contained in the set.
A main distinction can be made between sequential collections and associative collections.
In sequential collections, objects are collected in a sequential structure; the best-known
example is an array. Associative collections store not only objects but also an additional key
for each object through which it can be identified. An example of this is a dictionary.
2.5.10 Polymorphism
Object-oriented programming languages offer a rich set of constructs for modelling runtime
1
behaviour. Understanding polymorphism is key to designing scalable, plug-and-play architec-
tures. Polymorphism means that an operation may behave differently in different instances.
This is actually one of the cornerstones that has made object-orientation so powerful.
From a general point of view, polymorphism shows up in multiple methods having the
same name.
•In some cases, multiple methods have the same name, but different formal argument lists
(overloaded methods).
•In other cases, multiple methods have the same name, same return type and same formal
argument list (overridden methods).
1
Runtime is when a program is running (or being executable) – that is, when you start a program running in a computer, it is the
runtime for that program. Programmers distinguish between what happens in a program when it is compiled (compile time) and
what happens when it used or at runtime.

55. Exploring the Variety of Random
Documents with Different Content

56. He had known Mr Burlingame for two years as the doyen of the
diplomatic body, the most fervid champion of that "co-operative
policy" whereby the treaty Powers agreed to act as a united body in
pursuit of identical objects. He could not suppose that his late
colleague had turned his back on those common objects without
notice. Although, therefore, the suddenness and secrecy of the move
might have suggested misgivings as to the mission being intended to
promote the views of the diplomatic body in Peking, yet it is beyond
question that Sir Rutherford Alcock heartily favoured the embassy.
His confidence in it is further attested by a very long and elaborate
memorandum which he addressed to Prince Kung, indicating the
uses to which the embassy should be put in bringing about an
understanding with the Powers, whereby Chinese interests would be
safeguarded while the treaty rights of foreigners should be amply
fulfilled. "I see in the mission a hope of improvement and a material
change in the whole aspect of affairs.... Proves there are Ministers
with power and influence in the councils of the emperor who believe
the time has come for breaking with the past.... After a long night of
weariness and futile efforts, daylight begins to appear.... I hail the
appointment of a representative to the Western Powers as the
beginning of a new era." Such was the Minister's valediction in his
report to the Foreign Office. But he had been mightily deceived. The
night had indeed been long, but it was not the true dawn which was
welcomed with this joyful acclamation. How quickly the gloom
settled down again on that scene of fruitless toil will presently be
seen.
The mission was introduced to the notice of the world by a
humorous prelude, which may be quoted for the sake of the light it
incidentally throws on the chronic state of China. On their way from
Peking to Tientsin, seventy or eighty miles, the envoys halted at a
large market-town, where a report met them of a phenomenon not
very uncommon in those parts, especially in winter—a band of
marauders who had been annoying the neighbourhood. The mission
took refuge in an inn, resolved to stand a siege until aid should
come. In this strait Mr Burlingame seems never to have thought of

57. applying either to the local authorities of the town or to the
Government he was serving, but despatched urgent messages to
Peking, where there were escorts kept at the Russian and British
Legations, and to Tientsin, where was the British gunboat Dove. His
appeals were answered with alacrity from both sides. From Peking
came a relief party of British and Russian soldiers in charge of
members of the two Legations; from Tientsin a party of mounted
bluejackets under Lieutenant Dunlop. They met at the half-way
house where the mission lay, but nothing could be seen or heard of
the besiegers. Mr Burlingame's party reached their port of
embarkation without further adventure. Indeed the only serious
matter that arose out of the imbroglio was a difference of opinion
between one Vodkansky of the Cossack guard and Mulvaney, a
sturdy Hibernian of the British escort, which the latter proposed to
settle by the means in vogue among heroes before the days of
Agamemnon. Tragic consequences were, however, averted by the
soothing diplomacy of the representative of her Majesty's Legation,
Mr Conolly, and the two Burlingame relief expeditions returned to
their respective stations nothing the worse for a couple of days'
outing in the bracing November air.
Mr Burlingame made his début in the United States, first by eloquent
speeches in San Francisco, and next by what assumed the form of
serious negotiations at Washington. An orator cannot reasonably be
held accountable for every detail of his orations, but Mr Burlingame's
mission may be most favourably summarised by a few carefully
chosen words of his own:—
1st. It was the object of the mission to disabuse the foreign Powers of
an impression they were supposed to entertain, that the Chinese
Government had entered upon a retrograde policy.
2nd. To deprecate a precipitate and unfriendly attempt on their part to
enter upon a policy which might make all progress impossible from its
menacing tone and "violent shock to the feelings, and even
prejudices, of the people."

58. Translated into practice, these propositions meant that China wished
to be let alone; and that, we may safely assume, represented the
whole extent of Mr Burlingame's instructions. This claim was
embodied in a convention which he made at Washington, comprising
certain "additional articles" to the American treaty of 1858, the
purport of which was that the United States undertook to apply no
pressure to China, which, it may be presumed, that Power had never
the intention of doing. The convention was for several reasons not
welcomed at Peking, but it served the only purpose which perhaps it
was ever expected to serve, that of giving the keynote to the
representations which the envoy was afterwards to make to the
various Powers in Europe.
The next Government to which Mr Burlingame addressed himself
was that of Great Britain, over which he obtained a more important
success than over that of the United States. In fact, he persuaded
Lord Clarendon to discard all the information that ever reached the
Foreign Office from its own responsible agents in China—men who
were bound by every consideration of loyalty and public duty to
report only what was true, and to accept instead thereof the
protestations of an agent hired to make out a case; for it is
superfluous to add that Mr Burlingame was far indeed from
representing the true state of facts. He succeeded in so altering the
course of the British Government that their agent in China was
discredited, stultified, and rendered powerless to effect the objects
for which he had been labouring. This was the first step of the
Foreign Office in the new departure which had many evil results—
that, namely, of taking their cue not from agents in their own pay,
but from others over whom they could exercise no control, and who
had alien interests to serve.
From the Chinese point of view the Burlingame mission was a
decided success.

59. III. CHINESE OUTRAGES—YANGCHOW AND FORMOSA.
Missions attacked at Yangchow—Redress refused by Chinese and enforced by
consul—With naval assistance—Satisfactory issue—Continuous outrages in
Formosa—Government affords no relief—Disturbances quelled by British forces—
Lawlessness near Swatow—Communications with interior controlled by bandits—
Order restored by Consul Alabaster with naval force—Peace and good feeling
between Chinese and foreigners resulting from these various measures—Which
were approved by Imperial Government—Disapproved by British Government in
consequence of Mr Burlingame's representations—Consuls punished—Lord
Clarendon, prompted by Mr Burlingame, sends fresh instructions to Minister and
consuls.
The year 1868 was marked by serious anti-foreign outbreaks in
widely distant provinces of the empire. At Yangchow, a wealthy city
on the Grand Canal, twelve miles from the left bank of the Yangtze
river, a favourite resort for retired officials, rich salt merchants, and
gentry, the Inland missionaries under the orders of Mr Hudson Taylor
established themselves. In no locality in China could they have been
less welcome, for there they met their natural enemies in the
greatest force. Before long an attack on them was organised at the
instigation of the literati and gentry, and with the connivance of the
local authorities. "The onslaught was sudden and severe, the mob
set fire to the premises, the ladies and children of the mission had to
be thrown out of the windows to save their lives." There was no
mistake, therefore, as to the murderous intentions of the assailants.
The nearest British consul was at Shanghai, the consulate at
Chinkiang, twelve miles from the scene of the outrage, being in
charge of an assistant, Mr Clement Allen. That young officer
hastened instantly to the assistance of the missionaries, and made
his protest against the culpable negligence, to say no more, of the
Chinese officials, who on their part made a great to-do of hushing
the matter up and repairing the injured house. Consul Medhurst
promptly followed up the representations made by Mr Allen by
personal appeal to the viceroy at Nanking, fifty miles distant. The
mind of that high official had already been prejudiced by ingeniously
falsified reports of the transaction supplied to him by the prefect of

60. Yangchow, and in consequence he refused Mr Medhurst's request to
depute an official to accompany him to that city for the purpose of
investigating the facts. Thereupon Mr Medhurst, availing himself of
the arrival of H.M.'s ship Rinaldo at Chinkiang, obtained from her
commander a sufficient escort to accompany him to Yangchow; and
then only did the viceroy, Tsêng Kwo-fan, appoint an officer, though
of totally inadequate rank, to co-operate with the consul. The
Chinese officer did not, however, keep his appointment, and Mr
Medhurst proceeded without him, and placed in the hands of the
prefect at Yangchow a written demand for redress, one of the items
being the seizure and punishment of the gentry, whose names were
submitted. The prefect at once declared his inability to deal with
men of such influence, all being of higher rank than himself. As
nothing, therefore, could be settled at Yangchow, the prefect agreed
to accompany Mr Medhurst to Nanking to lay the whole matter
before the viceroy. A deputy from the viceroy, however, met Mr
Medhurst at Chinkiang and endeavoured to dissuade him from
proceeding to Nanking, offering instead to accompany him back to
Yangchow, according to the original programme. Mr Medhurst, in his
turn, persuaded the deputy to return with him to Nanking on H.M.'s
ship Rinaldo, which was to start from Chinkiang the following
morning. But the deputy Chang did not keep that appointment, any
more than he had kept his previous one. The prefect of Yangchow
also found means of evading his promise to accompany the consul
into the presence of the viceroy. After much pressure on the one
side and evasion on the other, the viceroy offered to settle the
matter by a charitable gratuity to the missionaries in lieu of
damages, and showed his anxiety to get the affair patched up
quickly by sending an official of rank to follow Mr Medhurst on board
H.M.'s ship Rinaldo, where he spent two hours in attempting to
persuade the consul to accept the terms offered. Matters were, in
fact, in a fair way of settlement when, "just at this juncture," the
commander of the Rinaldo fell sick and determined to proceed with
his ship to Shanghai, the consul being thus left in a humiliating and
helpless position, as Sir Rutherford Alcock describes it. The Chinese
officials at once changed their tone, withdrew from negotiations, and

61. nothing more could be done with them. The action of the naval
officer in abandoning the consul was freely criticised at the time, and
being in consequence asked by the Admiralty for an explanation, he
stated, among other things, "that it never entered his head that the
presence simply of a small man-of-war could have the effect of
influencing the viceroy." He also stated that he had "been given to
understand that the viceroy had expressed his willingness to comply
with Mr Medhurst's requests, and would send a letter to that effect
that night or the next morning." The gallant officer did not appear to
perceive that the withdrawal of his ship before the viceroy's promise
had been fulfilled completely changed the situation.
Nothing was left for the consul, then, but to lay the whole case
before H.M.'s Minister, and in doing so he made these observations:
"I can call to mind, out of my experience of British relations with
China, scarcely one instance in which the outrage complained of has
been more unprovoked on the part of the sufferers, and in which the
evidence of neglect and culpability on the part of the local
authorities has been more marked and incontrovertible. Few cases
can have occurred, moreover, in which the power to grant prompt
and reasonable redress was more within the reach of the supreme
provincial authority."
The Minister, in his turn, had no resource but to call upon the
admiral on the station "to repair the mischief by sending such naval
force to the mouth of the Grand Canal as shall enable him, if
necessary, to apply effective pressure both on the local authorities
and populace at Yangchow and on the viceroy at Nanking," to whom
the consul was once more instructed to address himself. Of course
the Minister had before this applied in the usual form to the Tsungli-
Yamên, and with the usual result. They deprecated hasty conclusions
until they themselves had full information from the local authorities;
but they admitted without hesitation that, assuming the facts, full
redress must be granted.
The Minister's representations to the Central Government were
renewed with greater emphasis on receipt of the news of the

62. collapse of the consul's negotiations. Prince Kung then expressed his
readiness to make the compensations demanded; but as regarded
the punishment of the instigators of the outrage, he contented
himself with tacitly indorsing the plea of the viceroy, "that the gentry
indicated were men of high rank, and incapable of wilful disregard of
treaty provisions, for which reason they need not be called to
account." In reply the Minister stated that immunity to such
offenders, more especially if highly placed, is wholly incompatible
with the treaty rights of foreigners. A new inquiry, however, was
instituted at Yangchow, and the Viceroy Tsêng, who had just been
gazetted to another post, was warned not to leave Nanking until the
affair was concluded. After an interval of two months, Consul
Medhurst, escorted by a naval force despatched to his aid by Admiral
Keppel, sent his cards once more to the Nanking viceroy. The old
tactics were repeated, and negotiations threatened to be indefinitely
protracted, but eventually promises were given for the full redress
demanded. Promises, however, had been given before, and it was
deemed not unreasonable in the circumstances to demand a
material guarantee. There happened to be lying at anchor opposite
the city a small steamer recently built for the viceroy, which he was
induced to place under the orders of Captain Heneage, R.N., pending
the execution of the arrangements. The end of the discussion was a
complete and satisfactory settlement of the whole affair, which
included the deprivation of the prefect and the magistrate of
Yangchow. The after-effects have been no less satisfactory. For the
last thirty years Yangchow has been the most peaceable missionary
field in the whole empire. We have set forth this incident in some
detail, because it was typical, isolated, and free from all obscurities.
While these events were passing on the Yangtze, similar troubles,
which had been threatening for some time, came to a head in the
island of Formosa. Outbreaks of mob-violence against the property
and person of both missionaries and merchants took place in
different parts of the island. At Banca, in the Tamsui district, two
English merchants, Messrs Kerr and Bird, were murderously
assaulted by a ferocious armed mob, and Mr Holt, the acting vice-

63. consul at Tamsui, reported in October 1868 that "remonstrance,
expostulation, despatches, letters, messages, and visits having alike
failed in securing common justice" from the mandarin, he might be
"driven at any moment to strike his consular flag and close
communication with the authorities. Our lives are threatened by
people who have proved that the will to murder us is not wanting,"
and with whom the authorities either could not or would not
interfere. Mr Holt held his ground until assistance reached him, and
he made no secret of his intention to back his diplomacy by a show
of force whenever he got the chance. "Short of destruction of life
and property," he wrote, "I intend using any means in my power to
enforce that justice that the people who are supposed to administer
it deny me. On the arrival of the gunboat I will at once inform your
Excellency of the measures concerted between the commander and
myself." Vice-Admiral Keppel reported to the Admiralty in December
that "the opportune arrival of H.M. gunboat Janus and the United
States Aroostook was followed by a full compliance with the
demands of her Majesty's consul."
Matters did not run quite so smoothly at the other end of the island,
where missionaries as well as merchants were the object of attack.
The campaign was carried on with vigour for some six months.
Redress was not only unobtainable from the Chinese authorities, but
even personal access to them was rendered impossible by the
obstruction of the mob. Mr George Jamieson was obliged to forego a
visit to the magistrate at Taiwan in April on the latter confessing that
he could not protect him from violence. Mr Gibson, five months later,
found his road to the mandarin ambuscaded by three parties of sixty
or seventy men each, armed with jingalls, swords, and spears.
Outrage succeeded outrage during the whole period. The state of
affairs was of course a subject of serious remonstrance with the
Central Government, of whom the Minister first demanded, as in the
Yangchow case, a joint inquiry into the facts. For this purpose the
consul, Mr Swinhoe, who had been absent on other duty, was
ordered to his proper post. At the same time Vice-Admiral Keppel

64. was requested to send an adequate naval force to support the
consul's position and prevent further outbreaks.
The Yamên went through the form of ordering to the spot a
commissioner, who, however, left it again immediately, thus turning
the orders of the Yamên into ridicule. This proceeding naturally
encouraged the hostility of the local officials and of the mob who
executed their behests. The situation became most threatening.
The squadron detached by Admiral Keppel for active operations at
Takow and its neighbourhood consisted of three corvettes and five
gunboats, to be reinforced if necessary by the flagship Rodney,
carrying eighty-two guns. Before this imposing force arrived,
however, the task they were intended to achieve had been already
accomplished. "Driven to despair, and believing life and property to
be in great danger, Mr Gibson, without waiting for instructions, called
upon Lieutenant Gurdon of the gunboat Algerine to take possession
of the Chinese fort, which resulted in a loss of life and a destruction
of Government stores."
Mr Gibson's action was somewhat euphemistically described as
"without waiting for instructions," seeing that he had positive
instructions to maintain his ground until a naval force should arrive.
Both the operation itself and certain details of its execution were
adverted upon so severely, first by Sir Rutherford Alcock and then by
the British Government, that, notwithstanding Commodore Jones's
commendation of "the most brilliant exploit I have heard of in these
seas," Lieutenant Gurdon fell under the displeasure of the Lords of
the Admiralty, as the acting consul did under that of the Foreign
Office. The object of the joint adventure, however, was attained, and
the spirit of outrage among the Chinese completely subdued. This
happened in December.
There remained, however, yet another centre of turbulence which
greatly impeded the operation of the treaty, at the port of Swatow.
The villages which lie between that seaport and the district city of
Chow-chow-fu, some 12 miles up the river Han, had banded

65. themselves together to oppose foreign intercourse with the latter
city. Not only were the business and property of foreign merchants
interfered with, but a British man-of-war gig in the river was fired
upon, and when the men landed to identify the offender they were
overpowered by the whole population of the nearest village. This
hostile attitude, resembling very much that of the Canton villages
twenty years before, steadily increased until the native officials
themselves were not safe in passing to and from the district city.
Strong representations were made to the high authorities of the
province at Canton. The viceroy had promised to send a military
force to quell the riotous villages, but before he had proved the
sincerity of his intention the Gordian knot was cut by British initiative
in January 1869. The late Sir Challoner Alabaster, a man of
uncommon resolution, was at that time acting consul at Swatow;
and he, having secured the co-operation of Commodore Jones, led a
force of marines and bluejackets against the offending villages. A
stout resistance was offered at first, but when several of the villages
had been taken and destroyed the whole eighteen made their
submission. Thereafter the district enjoyed perfect peace and
security. In the following March Sir Rutherford Alcock was able to
telegraph to Lord Clarendon that "the accounts from all the ports
showed that peace and order had been restored; that at Yangchow
and Formosa entire security and an improved position had been
obtained; that there was no more cause for anxiety at any point;
that the best understanding existed with the foreign body at Peking;
and that the relations with China had never been more satisfactory."
The bearing of these occurrences on the revision of the treaty may
not at first sight be quite clear, but it is interesting to note in what
manner they were connected with that operation in the mind of Sir
Rutherford Alcock. He calculated that the necessity of using force to
vindicate foreign treaty rights, of which both he and his predecessor
had constantly warned them, would bring home to the Peking
authorities the alternative which they would always have to face in
case of failure to carry out the treaties. How very differently these

66. outrages and the enforced redress affected the situation in Peking
will now be seen.
The action taken at Yangchow and in Formosa having been fully
explained to the Tsungli-Yamên, Wênsiang and the other Ministers
expressed their entire concurrence. But what satisfied the
Government of China produced quite another impression on that of
Great Britain. Lord Stanley, as Foreign Secretary, had written on
November 20, 1868: "Mr Medhurst appears to have acted with great
prudence and firmness, and you will convey to him my approval of
his proceedings.... I have to instruct you [Sir R. Alcock] to press the
case in question upon the Chinese Government." Two months later
Mr Medhurst was reprimanded by Lord Clarendon for his action, and
the "full satisfaction for the outrage" was attributed exclusively to
the "readiness with which the Central Government took measures
that proved effectual." The change of Government which had in the
interval taken place in England (December 9, 1868) was hardly
sufficient to account for so diametrical a change of view in a matter
of imperial concern. Another agency had effected the conversion of
the British Government. Mr Burlingame had arrived fresh from fervid
denunciations in the United States of the "tyrannic policy" and the
"throat policy" of Great Britain as applied to China, and adroitly
seizing on the repression of the Yangchow and Formosa outrages as
flagrant examples, he succeeded in incensing Lord Clarendon against
the various British officials concerned in these troubles, whom his
lordship visited with punishment which scarcely stopped short of
vindictiveness. Mr Medhurst, indeed, a man of long and
distinguished service, had only a black mark set against his name;
but Mr Gibson was publicly censured and degraded, and ordered to
make an apology to the Chinese officials whose lawless aggressions
he had lawlessly repelled. With some inconsistency, Lord Clarendon,
about the same time, approved the conduct of Acting-Consul Holt at
Tamsui, who succeeded in adjusting most serious misunderstandings
with the Chinese through no other means than the visible force of
the small gunboat Janus, for whose arrival he waited before
preferring his demands.

67. That the sudden change in the policy of the British Government was
the work of Mr Burlingame was frankly avowed by Lord Clarendon
himself, who based the fresh instructions to the Minister in China on
the arrangements he had concluded with the Chinese representative.
In his letter of condemnation, January 14, 1869, he, moreover,
intimated that he could not wait before pronouncing judgment for Sir
Rutherford Alcock's complete report on the Yangchow affair, because
his "communication with Mr Burlingame ... rendered it necessary
that he should not defer making his observations." That a British
Secretary of State could have so demeaned his office would not have
been believed save on his own confession. He of course carried the
Admiralty with him, and the same influence which inspired the new
instructions issued to the Minister and consuls inspired those issued
to the commanding officers on the China station.
Taken textually, the negotiations between Mr Burlingame and Lord
Clarendon were of a platonic character. H.M.'s Government
undertook to apply no pressure to China. It would have been a
simple matter to refrain from applying pressure, and a tacit
resolution to that effect with corresponding instruction to the
Minister in Peking would have secured the object. To make it a
subject of direct pledge to the Chinese Government seemed one of
those gratuitous acts which all diplomatic experience condemns as
fraught with future embarrassments. To save appearances, however,
a nominal equivalent was taken. "Mr Burlingame was requested to
bear in mind, and to make known to the Chinese Government, that
we should henceforward have a right to expect on its part the
faithful fulfilment of treaty engagements, the prompt redress of
grievances referred to the Central Government, and friendly
treatment of British subjects by the Chinese authorities"—as if all
that had not been already stipulated for under the solemn sanction
of the existing treaty.
IV. REVISION NEGOTIATIONS AND CONCLUSION.

68. Lukewarmness of British Government—Sir R. Alcock's misgivings as to success—
Mixed commission in Peking to consider details—Mr Hart's predominance—Treaty
becomes a custom-house concern—Increase of duties being the Chinese aim—
Sir Rutherford Alcock attributes failure to Mr Burlingame's misrepresentations—
Merchants oppose the treaty—Ratification refused by British Government—
Inferences from this fiasco—Chinese influenced by force alone.
Let us now revert to the cause and origin of the Burlingame mission
—the revision of the treaty of Tientsin. The instruction for revision
was given by Lord Stanley on August 16, 1867, in such general
terms as the following:—
Her Majesty's Government neither wish, nor have they the right, to
impose sacrifices on China, even though they may be convinced that
the inconvenience of such sacrifices will be only temporary, whereas
the benefit which will result from them will be lasting.... We must
reconcile ourselves to waiting for the gradual development of that
[better] system, and content ourselves with reserving for revision at a
future period any new arrangement we may come to in 1868.... You
will of course act openly with the representatives of other Powers,
inviting and availing yourself of their co-operation.
A note of misgiving as to the policy of asking for the revision runs
through the whole correspondence. After the preliminary labours of
sifting the voluminous memorials from merchants and others, Sir
Rutherford Alcock sums up their demands thus: "All their wants turn
upon three or four cardinal defects, not of the treaties so much as in
their execution." And he adds the significant reflection: "The
question arises, if nothing is to be gained by demanding a revision,
... whether much would not be lost, and an opportunity thrown
away, which might, by reserving the right, be turned to better
account when the emperor's majority is declared. I believe the true
policy of foreign Powers would be to wait; ... to this conclusion ... all
the representatives of foreign Powers now in Peking are led." "The
Chinese," he also says, "would go much faster and better if left
alone."
The question naturally suggested by these remarks—why a task
involving enormous labour, of which only negative results were to be

69. expected, was entered upon at all at such an inopportune moment—
remains unanswered.
It would be insufferably tedious, and of no practical utility, to track
the windings of a maze leading nowhere, for the revised treaty was
never ratified. But the labours of two whole years could not but
leave landmarks to guide succeeding travellers over the same
ground. It could not be but that with so much beating of the bushes
the game would be started, if not brought to bag. It was a
reconnaissance in force which, for the first time, compelled the
respective parties to the struggle to reveal their true character and
intentions. Such a discovery was perhaps not too dearly bought by
the time and trouble expended on it.
The first definite step in the process of revision was the nomination
of a mixed commission of British and Chinese "to devise means of
securing a more prompt redress of commercial grievances." The
members were Mr Fraser, second secretary to the British Legation;
Mr Hart, Inspector-General of Customs; and two secretaries of the
Tsungli-Yamên—a heavy preponderance on the Chinese side of the
question. To the same commission was added another British
member, Mr Adkins. And here it is not impertinent to observe that
the absence of both the Chinese secretary, Mr Wade, and the acting
Chinese secretary, Mr Brown, left the Legation in a condition too
crippled to engage on work which would have taxed its full strength.
The members of the commission held many sittings, reporting
proceedings from time to time to their respective principals, the
Tsungli-Yamên and the British Minister.
It needs no great effort of imagination to divine, in a body thus
composed, whose would be the dominant voice. Mr Hart conducted
the proceedings throughout. The discussion had not gone far when
it was found hopeless to revise the provisions of the treaty in any
sense compatible with progress or freer intercourse; and the
dangerous questions which had caused the Government so much
anxiety, and which had inspired both the Burlingame mission and the
various secret memorials, being thus happily ruled outside the

70. controversy, the Chinese Ministers seem to have given themselves
no further concern about the revision. This distant attitude of theirs
was severely commented on by a contemporary writer in 'Fraser's
Magazine,' who said:—
After ten years of conciliatory blandishments on our part, the high
Chinese authorities had so far disobeyed the spirit of the treaty that,
although they had not actually prevented our Minister from
corresponding and visiting with them, yet they had had the audacity
to render all such intercourse absolutely nugatory, and had
constrained him, after a long and successful diplomatic career, to
descend to the extremely humiliating position of treating with them
indirectly through the medium of Mr R. Hart.
As, however, the proceedings became focussed on a tariff revision
destined to add to the duty receipts, a "collector of revenue wanting
money," as Mr Hart described himself, was the most fitting
negotiator, and the Chinese ministers were well pleased to leave him
free to make his own bargain, so long as it yielded that result.
To give colour to the Chinese demand for higher duties a bold
formula was resorted to, and supported by equally bold reasoning.
The expedient was a rearrangement of the method of collection of
inland dues on foreign merchandise, which was then, as it continues
to be, the great bone of contention between foreign traders and the
Chinese authorities. The treaties conferred on merchants the right of
compounding for all inland taxation of their merchandise by a single
payment at the port of entry; but the practices of the Chinese
officials had rendered the privilege a nullity. In the new negotiations
Mr Hart, on the part of the Chinese, took the high ground of
maintaining, with subtle dialectic, that the protection which
foreigners claimed was not in fact given by the treaties. So strongly
did the Chinese entrench themselves in this contention, that heavy
artillery was required to dislodge them. "Could any negotiators be so
dull or incompetent," wrote Sir R. Alcock in reply, "as to sign a treaty
of commerce with an Eastern potentate, extorted at the point of the
bayonet, and leave this unlimited power in his hands to turn against
us the next moment, or whenever he pleased, and nullify all that

71. had been stipulated, destroying the trade for which alone war had
been made?" Defeated in argument, the Chinese next begged that
what they could not claim as a right might yet be accorded to them
as a favour, thus copying the tactics of the Japanese in an analogous
case.
As this proved to be the crux of the whole transaction, the rock on
which the convention eventually split, it is useful to consider how the
subject was treated in the negotiations. The treaties of Nanking,
1842, and of Tientsin, 1858, provided for the transit of British goods
throughout the empire on payment of a fixed charge. But in securing
exemption from arbitrary imposts in the interior, the treaty of
Nanking signally failed; that of Tientsin had proved equally
ineffective, and why? From inherent difficulties in the nature of
things—obstacles absolutely insuperable so long as the country
remained under the same organic conditions. Such were the
propositions with which the British Minister entered upon the
discussion of the subject; and as no proposal was made for changing
the organic conditions of the empire, the prospect of obtaining a
satisfactory fulfilment of those treaty provisions did not seem very
encouraging.
But then a suggestion, apparently emanating from Consul Robertson
at Canton, was made for simplifying the problem by doing away with
the option which had been reserved in the treaties for foreign
merchants, either to pay the commutation at the port of landing, or
to allow their goods to run the gantlet of the Chinese customs
stations. Instead of this, it was suggested that a single compulsory
payment, amounting to half the import tariff, might be levied on the
landing of the goods, which should thereafter be freed from all other
imposts throughout the empire. It was not unnatural that a
"collector of revenue" should appropriate this conception, and
introduce it into the revised treaty; but then the doubt immediately
arose on the other side, whether the promised exemption would be
any more of a reality than it had been under the existing régime. If
the difficulties in the way of fulfilling the stipulation in the treaty of

72. Tientsin and Nanking were really insuperable, would they now
disappear merely because the Chinese Government received an
increased import duty? In considering Mr Hart's proposal, "the
question would be," according to Sir Rutherford Alcock, "Could we
obtain a sufficient guarantee that such additional import due would
effectually exempt British goods from all other dues, local, provincial,
and what not?" And again, "Security for exemption from all but the
fixed 2½ per cent was the one question on which depended the
value of any revision."
A necessary condition of any successful treaty was the assent of all
the other Powers to its provisions, seeing that under their most-
favoured-nation clauses any one of them by holding aloof could
render the treaty inoperative. The various foreign representatives
were therefore kept informed of the progress of negotiations. In this
way their opinions were obtained from time to time as to the merits
of the various proposals. On the subject of the compulsory payment
of transit dues the opinions which the British Minister received from
his colleagues were all unfavourable. They considered that some
"additional guarantee would be necessary against failure, and as
against security for additional losses which would be entailed upon
the merchants." To give effect to the new proposals an edict was to
be published acquainting all provincial officials with what had been
agreed upon. But still the diplomatic body maintained "that nothing
is really certain but the addition of 2½ per cent to the import duties.
This will be rigorously exacted and paid; but whether the equivalent
exemption from all other taxation will be obtained must be held
doubtful, ... seeing that in the past the same provincial authorities
have shown the most persistent disregard of treaty stipulations and
proclamations." "Under such circumstances," Sir Rutherford adds, "it
would seem reasonable that, during the first year at least, all
amounts collected under the new arrangements ... should be carried
to a separate account ... to meet claims for compensation." In the
end, however, he saw reason to waive this proviso, to disregard the
views of his colleagues, and to assent to the new impost, without
any guarantee. Attempts to obtain concessions from the Chinese in

73. the way of freer intercourse proved, as we have said, hopeless from
the first. The renewal of the Chinese demand to establish a customs
station in Hongkong—that "immense smuggling depot"—was refused
on the British side; while the British request for recognition of
Hongkong as a port of call for goods in transit to Canton was in like
manner refused on the Chinese side, because it "would give the
place a respectable name" as well as make it the "great emporium of
the south." Hongkong, it is fair to remember, was, not unnaturally,
odious in the eyes of the Chinese. The more prosperous the colony
became, the more they hated it; and the more patriotic among them
—as, for instance, the Minister Wênsiang—detested it the most.
The ruling factor in eliminating all measures of progress from the
negotiations and reducing the whole to a customs question was Mr
Burlingame.
After the arrival of the mission to Washington [wrote Sir Rutherford on
February 27, 1869] the hopes which the signature of the additional
articles was calculated to excite undoubtedly exercise a very
prejudicial effect on my efforts.... With Mr Burlingame's enthusiastic
reception, and the prompt signature of the convention by which the
United States Government pledged itself to leave China free to adopt
or reject all such innovations and internal improvements, and even to
use its influence with other Powers for the same end, they gained
precisely the assurance they wanted.... From that moment further
progress or successful negotiation became impossible.
He added in a subsequent despatch to Lord Clarendon:—
One result stands out more clearly than any other, and it is this: what
we have gained by the last year's preliminary negotiations is not likely
to be withdrawn. But if it was difficult to negotiate for large
concessions before the assurance authoritatively given by your
lordship to Mr Burlingame, ... it is now out of the question to hope for
more than has already been conceded.... Strong in the assurances of
two of the treaty Powers, ... it is quite certain that no further progress
can be made at present. It simply remains for her Majesty's
Government to determine whether they will carry out the revision on
the basis proposed and already assented to by the Chinese
Government, or defer the revision altogether to some later period.

74. The provisional report of the negotiations having been submitted by
the Foreign Office to the other treaty Powers for their opinion, most
of them contented themselves with amicable generalities, the only
definite criticism elicited being that of the North German
Confederation. Going straight to the core of the matter, in May 1869,
Count Bernstorff wrote as follows, basing his remarks upon the
opinion of the German merchants:—
Although the advantages which are to be expected for trade in
general from the abolition of the "lekin taxes" would not be too dearly
bought by this extension of the transit duty to all commodities, yet, on
the other hand, the treaty Powers certainly have the right of
demanding the abolition of the taxes levied contrary to treaty, even
without giving anything in return, and they might probably obtain this
result by common action. And then, moreover, it appears, from
existing circumstances in China, exceedingly questionable whether
this tax, even if abolished by imperial edict in consequence of a treaty,
would not, nevertheless, still be levied by the mandarins, although
perhaps in another shape, since now indeed they have their
assignments thereon.
Doubts on the part of the Foreign Office led to further
correspondence backwards and forwards, closing with the following
ambiguous despatch, dated 29th September, which was transmitted
by telegram, a very slow process in those days:—
If you should not have concluded an arrangement before this reaches
you, her Majesty's Government think it would be better to protract
negotiations rather than accept now a limited arrangement, which
would be binding for so long a period as ten years, and which would
not comprise a satisfactory arrangement respecting transit duties, and
which might compromise the right of her Majesty's Government to
take part in the negotiations of other Powers for a revision of their
treaties.
Should you, however, have completed any arrangement, you may be
assured that the best view will be taken of it here.
The supplementary convention was, in fact, signed in October, and
Sir Rutherford Alcock took his leave immediately after, visiting the
Yangtze, Shanghai, Hongkong, and India on his way to Europe. At

75. these places he explained in general terms the bearing of the treaty,
the Indian Government being specially concerned in the increase of
the Chinese import duty on opium, to which the trade generally were
absolutely indifferent.
The supplementary convention was exhaustively reviewed by the
Shanghai General Chamber of Commerce in a memorial addressed to
Lord Clarendon (December 31, 1869). To the practical view of the
merchants the treaty consisted of three clauses: one making
compulsory what had previously been optional—the payment of half
the import duty in commutation of inland dues on foreign
merchandise; one doubling the export duty on raw silk; and the third
more than doubling the import duty on opium. Of these, the first
alone was deemed important. The consideration offered by the
Chinese Government for the compulsory payment—that they would
frank imported goods through nine of the eighteen provinces of
China—was not regarded as an equivalent; for the treaty of Tientsin
contained the same undertaking without the geographical limitation,
but it had not been fulfilled. The ground alleged for this non-
observance of the existing treaty had been the existence of
insurmountable obstacles in connection with provincial and imperial
finance. These obstacles, the merchants observed, were "now
assumed to have been suddenly overcome," an assumption which
they considered illusory. The question of transit dues was not new to
them: it had been threshed out on all sides during weary years; it
was the recurrent topic of the day with them, as it was destined to
continue to be for a generation longer; and the merchants could not
therefore believe that the difficulties against which they had been
hopelessly struggling were suddenly removed by magic. They were
not shown how the revolution was to be effected. In short, "the
conclusion," they said, "was irresistible, that to a very great extent
the commutation of transit dues, which is made compulsory by the
new treaty, will simply become an additional tax on trade without
any return whatever; and that the provincial authorities will as
heretofore tax goods in transit very much as they please, the treaty

76. stipulation to the contrary notwithstanding,"—a conclusion supported
by arguments which could not be refuted.
Sir Thomas Wade some years later expressed the same views as the
merchants had done. "I doubted," he said, "the good faith of officials
when breach of faith could only be established by the evidence of
those subject to their authority and entirely in their power.... I have
since found reason to believe that the control of taxation in the
provinces is a matter of no small trouble to the Central Government
as at present constituted, if indeed it be possible at all."
Nevertheless, he adds, "I have found occasion to regret that the
convention has not been allowed at least a term of probation." A
term of probation was the alternative suggested by the merchants
also, but it seems never to have received any consideration from the
Foreign Office.
The representation which the Shanghai Chamber of Commerce
based upon their review of the treaty was adopted by influential
commercial bodies in England, who in a "monstrous deputation," as
Mr Hammond called it, urged on the Secretary for Foreign Affairs the
non-ratification of the treaty. The British Government gave way, not,
as they candidly admitted, convinced by the reasoning, but
overawed by the electoral pressure of the merchants; and the
supplementary convention was allowed to fall through.
Thus ended the first attempt to negotiate a treaty with China as a
perfectly free agent. The conclusion to be drawn not only from the
negative result, but from the whole process of the negotiations—
from the memorials from the provinces, and still more from the Privy
Council, the six boards, and the censorates—is, as stated by Sir
Rutherford Alcock in May 1869, "that the old spirit of arrogance of
the days of Lin and Yeh is still in full vigour, and the assumption of
superiority over the barbarian absolutely unmeasured. That the anti-
foreign element amongst the official and educated classes has
suffered no diminution whatever; that if some two or three leading
men take a clearer view of the political situation, they are evidently
without power to take action upon it; and so the vessel of State is

77. allowed to drift whichever way the tide of prejudice and ignorance
may set. There are still some documents," he added, "wanting to
complete the series, especially the answer of Li Hung-chang and a
second memorial of Tsêng Kwo-fan [p. 184 seq.], which it would be
desirable to obtain as showing the policy advocated by two of the
most prominent men in the empire at this moment."
One sentence of Sir Rutherford Alcock sums up the case China v. the
West: "Pressure, indeed, there must always be here if anything is to
be achieved for the advancement of foreign interests and commerce.
In one way or other, however we may disguise it, our position in
China has been created by force—naked, physical force; and any
intelligent policy to improve or maintain that position must still look
to force in some form, latent or expressed, for the results." Whether
the Western nations, singly or collectively, are justified in using their
force for such a purpose is a question which is not affected by this
plain statement of the case. That the policy of the Western Powers
has been largely influenced by sentimental consideration towards
China is true; but their action has never been consistent with their
professions, and their oscillation between coercion and submission
has led to disastrous consequences.

78. CHAPTER XXII.
MISSIONARY PROBLEM—TIENTSIN MASSACRE OF 1870.
Importance of missionary question long foreseen by Consul Alcock—Introduction
of missionaries under two French treaties—Toleration of Christians under treaties
of 1858—Forced upon China—Ardour of missionary spirit uncontrollable—
Negligence of treaty-makers in providing no regulations for admission of the
propaganda—Contrasted with the care bestowed on trade regulations—Religious
toleration of the Chinese—Christian intolerance—Surreptitious article in French
Convention of 1860—Giving large privileges to missionaries in the interior—Its
abuse complained of by Chinese—Enforced restitution of old property—Bitter
injustice—Disintegrating action of the propaganda—Abuses of extra-territoriality
—Interference in local affairs—Detaching natives from their allegiance—Causes
of strife—Chinese Government culpable in permitting abuses—Disputes about
land and houses—Chinese official laxity compensated for by unofficial
illegitimate methods—Attacks on missions fomented thereby—No remedy
possible without the unanimous consent of the Powers—Each having different
objects—Fruits of widespread hostility to missions appeared in 1868—Riot and
outrage—Culminated in Tientsin massacre of 1870—Details of the occurrence—
Treated cavalierly by Imperial Government—Culpability of officials—Pressure by
foreign Ministers induces Chinese to execute sixteen criminals—Apologetic
mission of Chunghou to France—Suspicions of his complicity unfounded—Causes
of the hostility to foreigners—Government fear of reprisals by France—They
begin to take the missionary question seriously—Issue an important circular—
Badly received by the Powers.
No subject more seriously engaged the attention of Sir Rutherford
Alcock during his whole term of service than that of the Christian
propaganda. While it was yet in embryo, and long before the
untoward consequences now so familiar had declared themselves,
the evil to come formed the theme of many anxious despatches. For,
with the exception of Mr T. T. Meadows, he was the only one of the

79. early consuls who attempted to read the horoscope of China with a
conscious participation in the responsibility for its welfare. Their
warnings were, of course, wasted on the desert air, for statesmen
whose hands are on the lever of events are like the signalmen on a
busy railway, recking nothing of the origin or destination of the train,
careful only that it pass their own "point" in safety. The thin end of
the entering wedge destined to split China into fragments, unless
anticipated (as in fact it has been) in its disruptive work by some
ruder allied agency, was clearly discerned by Consul Alcock while at
Shanghai. Under cover of the first French treaties in 1844 and 1846
missionaries effected a legal lodgment on the coast of China, from
which they cast longing eyes on the vast interior of the country.
Rivalry between the Christian sects brought fresh pressure to bear
on the plenipotentiaries, and the "toleration clause" was introduced
into all the treaties negotiated at Tientsin in 1858, and in the
German treaty of 1861.
Russia led the way, followed by the United States, Great Britain, and
France. The "clause" was substantially the same in all, the toleration
of Christianity being based on its moral character exclusively
—"Hommes de bien qui ne cherchent pas d'avantages matériels"
(Russian); "Teaching men to do good, and to do to others as they
would have others do to them" (American); "Inculcates the practice
of virtue, and teaches man to do as he would be done by" (English);
"Ayant pour objet essentiel de porter les hommes à la vertu"
(French).
[16]
Yet this apparent unanimity concealed essential
differences in aim and motive. Russia, France, and the United States,
to leave England out of the account, each meant something
specifically distinct from the other by the practically identical clause.
What the Chinese would have said, had they been free to discuss
the demand made upon them, we can hardly conjecture; but in the
position in which they actually found themselves they would have
subscribed to any form of words submitted to them, their sole
anxiety then being to get rid of the barbarians on any terms. Had
the preamble run, "Whereas the Christian religion as practised for

80. 1800 years has not brought peace but a sword upon the earth, has
set the father against the son, nation against nation, instigated
crimes without number, sided with the oppressor and the
unrighteous judge, and is daily prostituted for political ends," the
Chinese would have signed the toleration clause just the same. The
phraseology was nothing to them, whence it follows that the
responsibility for the consequences rests on the Powers who
imposed the form as well as the substance of the obligations. These
Powers placed themselves in a self-contradictory position both
towards China and the Church, for the only ground on which they
claimed protection for missionaries in the framing of the treaty is the
one which they cannot so much as consider in the fulfilment of it.
The ethical and religious side of the propaganda is to the executive
official a negligible quantity, while he can take cognisance only of
that aspect of Christianity which was studiously kept out of sight in
the treaty—its political character, the temper of the missionaries and
of the people among whom they work, and all that makes for good
or bad relations between them.
Amid mixed and perverted motives there is doubtless in all sections
of the propaganda a residuum of pure zeal in a holy cause. The
medieval solicitude for "saving the heathen" survives, and men and
women, fired with the conviction that they are engaged in such a
godlike enterprise, constitute an ever-living force with which
statesmen have to lay their account. It can neither be reasoned with
nor turned aside, and is the more intractable in that the logical effect
of its inspiration is to place it above civil law, but under a divine law
of its own interpreting, the interpretation varying indefinitely with
the divisions of the force, each division, and sometimes each
individual, selecting such portions of the code and bending them to
such meaning as may support the objects and the methods of the
sect. To introduce such a complex ferment into the Chinese body
politic was a psychological experiment on a colossal scale, and also
irrevocable. It was, therefore, an experiment which demanded the
kind of precaution used in handling dangerous chemicals.

81. Yet absolutely no thought was bestowed on the subject; the
explosive was imported with less ceremony than is bestowed on a
bale of long cloth, and left to spread according to its own laws in the
living tissue into which it was injected. So far at least as the English
treaty was concerned, we have it on the authority of the actual
negotiator that the Christian clause was an after-thought "shoved in"
at the last moment. The same authority adds, "The treaty was left to
carry out itself"—in other respects besides that of the missionary
question. Sir Rutherford Alcock speaks of "the futility of grafting on
to a treaty of commerce, forced upon the Chinese under
circumstances which left them no power to refuse, a proselytising
agency for the conversion of the nation to Christianity.... Whatever
aims at these ends under the stipulation of a treaty of commerce
and amity introduces a cause of distrust and an element of
disturbance. This we have done, and are now reaping the fruit." But
a rose-cutting would not be grafted with the insouciance with which
this spiritual element was incongruously inserted in a commercial
treaty. Commenting directly upon the toleration clause itself, Sir
Rutherford wrote: "It is only necessary to read carefully the words of
the article to be aware that in the whole range of the treaty, from
the 1st to the 56th article, there is nothing stipulated for so difficult
to secure as the fulfilment in its integrity of this one clause."
The foreign Powers generally seemed to court the very "disturbance"
apprehended by "leaving the treaty to carry out itself," washing their
hands of their own careless work. We have seen what pains were
taken to allow the treaty to operate smoothly in its main purpose by
elaborating a scheme of trade regulations far more complete than
the treaty itself. But as foreign trade had been carried on by the
Chinese for centuries, and the merchants of the respective countries
were thoroughly at home with each other, commerce was the least
likely source of friction. Of the new dynamic element introduced into
the treaties, it seems never to have occurred to the negotiators that
any regulation was necessary at all. Missionaries were permitted to
enter and settle in the interior, where everything was strange, for
practical purposes beyond the orbit of their countries' laws, while

82. protected against the jurisdiction of the Government under which
they were to live. Men who could withstand the temptation offered
by such a state of things are not born every day. Without rule of
conduct save their individual judgment, with no previous
understanding with the Chinese provincial officials as to relative
rights and duties, they were left to find such accommodation to their
surroundings as their several idiosyncrasies and the untried
conditions of Chinese social life might determine. The missionary in
the interior had thus all the qualities of a "foreign body" setting up
irritation in the organism,—a state of things, however, which his
absolute faith in the sanctity of his mission perhaps prevented him
from comprehending.
One trait in the national character was highly favourable to the
reception of a foreign religion. The Chinese were of all nations the
most tolerant of opinion. They had already accepted and assimilated
two foreign religions—Buddhism and Mohammedanism; indeed they
had also, two hundred years before, accepted and retained
Christianity until it was expelled in convulsions provoked by the
foreign missionaries themselves. Its second advent need not have
caused convulsions had it come as the others had done, with clean
hands, as a religion and nothing else. The tolerance of the Chinese
has been referred to materialism and contemptuous apathy, which is
by no means an exhaustive account of the matter. They were not,
any more than Hindus, naked savages without language or
literature: if anything, they were over-civilised. Proud they were,
indeed, and conceited, and in its religious aspect they affected to
regard Christianity as but a wave breaking on a rock. Their rock was
a unique philosophy, scarcely to be called a system, which stands for
religion, differing from other philosophic systems in eschewing
speculation and attending to the ethics of common life,—the only
philosophy that may be said ever to have transfused itself into the
blood of a people.
The culture of the Chinese, however, was merely an obstacle to the
realisation of the Catholic ideal of saving the heathen, as the

83. grandest natural scenery was regarded merely as a hindrance to
medieval travel. "Unhappy infidels, who spend their lives in smoke
and their eternity in flames," was Father le Jeune's epigrammatic
summary of the whole case in Quebec. So deep-rooted is the
tradition of the reprobation of the heathen, that it generally requires
many years' experience before a foreign missionary is led by contact
with facts to see that Chinese ethics form the natural basis for the
Christian superstructure. Some missionaries, indeed, go so far as to
use the writings of Confucius as a text-book. Before reaching this
ripe stage, however, the foreign missionary has it in his power to do
more mischief than he can perhaps ever undo.
There was one treaty stipulation which has not been left to chance
for its fulfilment—the additional article inserted in the French
Convention of Peking in 1860. An astute missionary, acting as
interpreter to Baron Gros, managed to interpolate in the Chinese
text a clause of his own which had no place in the French—the ruling
version—and was quite unknown to the French Envoy.
[17]
By that
clause full permission was accorded to French missionaries to
purchase land and erect buildings thereon throughout the empire;
and further, all churches, schools, cemeteries, lands, and buildings
which had been owned by persecuted Christians (Chinese) in
previous centuries were to be paid for, and the money handed to the
French representative in Peking for transmission to the Christians in
the localities concerned. This astounding demand, in our eyes at
once so truculent and so impracticable, seems to have been to the
Chinese neither more nor less oppressive than the rest of the treaty,
and they signed without demur, under the usual mental reservation.
But it was in germ an official recognition of a French protectorate
over Chinese Christians, and of corporate communities of Christians
held qualified to be served heirs to those who had been persecuted
in the seventeenth and eighteenth centuries—a germ which might
be cultivated with greater or less success, according to the skill of
those who had the care of it. Some effort of imagination is required
in order to realise what is implied in this surreptitious article.

84. We must suppose [wrote Sir Rutherford Alcock] a French army
entering London and there dictating the conditions of peace, and
among others one that all Church property confiscated by Henry VIII.
should forthwith be restored to the Roman Catholic Church by the
present holders, however acquired, and without compensation, and
that the French Government could be appealed to in order to enforce
the rigorous execution of the stipulation.
How the stipulation was enforced is thus described by Prince Kung in
his circular of 1871, more fully noticed below:—
During the last few years the restitution of chapels in every province
has been insisted upon without any regard for the feeling of the
masses, the missionaries obstinately persisting in their claims. They
have also pointed out fine handsome houses (belonging to, or
occupied by, the gentry or others) as buildings once used as churches,
and these they have compelled the people to give up. But what is
worst, and what wounds the dignity of the people, is that they often
claim as their property yamêns, places of assembly, temples held in
high respect by the literates and the inhabitants of the
neighbourhood. Buildings which were once used as chapels have been
in some cases sold years ago by Christians; and, having been sold and
resold by one of the people to another, have passed through the
hands of several proprietors. There is also a large number of buildings
which have been newly repaired at very considerable expense, of
which the missionaries have insisted on the restitution, refusing at the
same time to pay anything for them. On the other hand, there are
some houses which have become dilapidated, and the missionaries
put in a claim for the necessary repair. Their conduct excites the
indignation of the people whenever they come in contact with each
other, and it becomes impossible for them to live quietly together.
[18]
Bitter consequences have resulted from the enforced operation of
the interpolated clause, for the French Government, as is shown
above, took full advantage of the pious fraud. Neither did the
Chinese themselves, on discovering the truth, openly resent this
example of how the foreign religion "porte les hommes à la vertu."
The fraud was more than condoned by missionaries of all nations
and sects, whose legal title to residence in the interior of China,
distant from all authority, rests solely on the interpolated French
clause, the benefit of which accrues to them under the most-

85. favoured-nation privilege. British Protestant missionaries, not
altogether satisfied with this tainted title, in a long letter to their
Minister, Sir Rutherford Alcock, claimed the right of inland residence
on another ground. They adduced the public declaration of Mr
Burlingame, that "China invites Protestant missionaries to plant the
shining Cross on every hill and in every valley"; to which the answer
was simple, that the Chinese Government disavowed the promises of
the envoy, and repudiated the implied obligation. The British
Government disapproved of the claim under the French treaty,
though in rather ambiguous terms, because it rested "on no sound
foundation, but on an interpolation of words in the Chinese version
alone in the French treaty with China." Since then, however, the
pretensions of the French missionaries have been vindicated less by
the interpolated clause itself than by the vigorous exercise of all the
rights conferred by it, and very much more. The clause thus lent
material force to the spiritual ferment, accelerating by many degrees
its disintegrating action. It may be alleged, in palliation of the light-
heartedness with which the whole subject was treated by the
negotiators of the treaties, that they could not have foreseen such a
development of their innocent toleration clause; but the
circumstance only emphasises the urgent need there was for a clear
definition of what was really meant by it.
But if toleration be the note of Chinese polity—concerning not
religion alone, but almost every matter affecting government—it may
be asked, What is it in the propagation of Christianity that excites
the hostility of people and rulers? It is that the missionaries present
themselves to Chinese view as the instruments of powerful nations
bent on the ruin of the empire. They enter the country with a
talisman of extra-territoriality; their persons are sacred; the law of
the land cannot lay hands on them. That is the first stage. The
second is, that they seek to extra-territorialise their converts also,
whose battles they fight in the provincial courts and in the rustic
communes, and so make it of material advantage to the people to
bear the banner of the Cross. Many missionaries are really zealous in
the work of alienating the Chinese from their natural allegiance, and

86. of encouraging them to seek the protection of foreign Powers as
against the native authorities. Thus a revolution of the most vital
nature is in progress, and is being pushed on with all the energy
which Christian, combined with ecclesiastical and political, zeal can
throw into the work. Village is set against village, clan against clan,
family against family, and a man's foes in China are too often they of
his own household.
[19]
No doubt the Chinese Government are to blame for having allowed
such a state of things to grow up; but it is part and parcel of their
drifting attitude towards everything. It is not that their
apprehensions are not aroused, but that they lack initiative to avert
the danger which they fear. While in theory they do not admit the
claim of any foreign Power to protect Chinese subjects, yet in
practice the thing goes on, and is acquiesced in. So formidable,
indeed, have the foreign missionaries become, that most of the
provincial authorities are afraid as well as jealous of them; and
peace-loving viceroys give the simple injunction to their prefects and
magistrates that on no account must they permit dispute with
foreigners or native Christians. This means that the Chinese Christian
must be upheld, right or wrong, and the Christian would be very un-
Chinese if he did not take advantage of such a privilege to trounce
his heathen neighbours.
The right given in the French treaty of acquiring land and building
houses in the interior is one of the most constant causes of local
quarrel. Real estate in China, being held not on personal but on
family tenure, can only be rightfully alienated by the common
consent. A dissentient member holding out, or reviving his claim for
purposes of extortion after assent has been given and transfer
made, may become a convenient instrument in the hands of
agitators against the foreigners; and where there is no such
dissentient it is not unusual for the local authorities to create one by
forcible means. A case in point may be mentioned in illustration. A
building was made over to the Baptist Missionary Society by a
Chinese family, every precaution being taken to obtain the

87. unanimous consent of its various branches. When the deed had
been signed by the head of the family and other responsible
members, the local magistrate examined the chief of the clan,
denounced him, and punished him severely by bastinado. Two of the
signatories, thus intimidated, disowned their own act, thereby
invalidating the deed by non-unanimity.
Nearly all the attacks on missionaries proceed in one form or another
from that fecund nursery of feuds, the land question. Whatever the
merits of the dispute, the foreigner is prima facie in the wrong; for
he is an alien, an intruder, and he erects buildings which are
outlandish, offensive to taste, and of sinister influence; and
whosoever, albeit the most disreputable member of a family of three
or four generations, proclaims a grievance by which he has lost his
birthright, is sure of a sympathetic following. Thus without taking
into account individual indiscretions, or infirmities of temper, open
attacks on time-honoured customs, and so forth, there is a perennial
root of bitterness in missionary enterprise in the interior of China,
which throws out shoots culminating in murder and fiendish ferocity;
and all this without even a distant approach to the kernel of
Christianity which lies behind the outworks.
For what the Chinese authorities have failed to do by the legitimate
means at their command, their underlings and the circle of gentry
that surrounds each provincial centre attempt to do by illegitimate
and criminal methods. Hatred of missions and converts shows itself
by violent outbreaks in which innocent and guilty suffer a common
fate; mobs are excited by false suggestions, scholars write
inflammatory placards filled with the foulest calumnies, and the
higher officials "let it work"—secretly applauding, but ready, if called
to account, to exculpate themselves and blame the poor ignorant
people.
The charges which form the staple of these attacks turn largely upon
the murder of children in order to make use of eyes, members,
blood, &c., in certain Christian rites; and they are so extravagant and
absurd that foreigners are apt to doubt that even the most ignorant

88. among the people really believe in the crimes which are alleged
against Christians. The best authorities, however,—as, for example,
the late Sir Thomas Wade,—do not question the sincerity of the
popular belief; and indeed if we compare these charges with those
made against the Jews by influential sections of Christians in Europe,
we shall be surprised at their practical identity.
For this deplorable state of things no one has been able to suggest a
remedy. What has been done cannot be undone. To mend it even
would require such united action among the Great Powers as it is
hardly possible in the present state of the world to conceive. France,
indeed, on the morrow of the Tientsin massacre, did appeal to the
co-operative principle as a protection to all foreign interests in China.
The French ambassador in London addressed the Foreign Office in
these terms:—

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