Put call parity relation

1. Put Call Parity Model 1 The prices of European puts and calls on the same stock with identical exercise prices and expiration dates have a special relationship. The put price, call price, stock price, exercise price, and risk-free rate are all related by a formula called put-call parity

2. 2 Variable Definitions C = call premium P = put premium S = current stock price S 1 = stock price at option expiration E = option striking price R = riskless interest rate t = time until option expiration

3. 3 The Put/Call Parity Relationship We now know how the call prices, put prices, the stock price, and the riskless interest rate are related:

4. 4 The Put/Call Parity Relationship The interpretation of this is as follows: Buying a call and shorting a put is the same as: Buying the stock and borrowing E (the exercise price) at the risk free rate

5. 5 The Put/Call Parity Relationship (cont’d) Equilibrium Stock Price Example You have the following information: Call price = $3.5 Put price = $1 Striking price = $75 Riskless interest rate = 5% Time until option expiration = 32 days If there are no arbitrage opportunities, what is the equilibrium stock price?

6. 6 The Put/Call Parity Relationship (cont’d) Equilibrium Stock Price Example (cont’d) Using the put/call parity relationship to solve for the stock price:

7. 7 The Put/Call Parity Relationship A stock trades at $50 with a six month put option (strike price=$50) trading at $4.25. If the interest rate is 3%, what is a six month call option trading at?

8. 8 The Put/Call Parity Relationship A stock trades at $60 with a put option (strike price=$60) trading at $2.75. If the call option trades at $5.35, what is the interest rate?

9. 9 Making Arbitrage Profits A stock trades at $25 with a put option (strike price=$25) trading at $3.00. If the call option trades at $3.50 and the interest rate is 5%, how do I make a riskless profit? How much of a profit do I make for each share traded ? Buy stock, buy put, short call, borrow money Profit per share = $24.75-$23.81 = $0.94

10. Thank you 10