Black Scholes Model Option Pricing Method

Black Scholes Model

1. Black Scholes Model For Option Pricing

2. Introduction Also known as Black-Scholes-Merton model. The Black-Scholes model is a formula used to calculate the fair price of options , which are financial contracts that give the right (but not the obligation) to buy or sell a stock at a certain price on or before a set date. Based on five variables (Current spot price, strike price, risk free interest rate, time to maturity and volatility) Originally, developed for European options.

3. From the following information, calculate the option premium for one share. Current stock price = Rs 100 Strike price =Rs 95 Time to maturity = 6 months Risk free interest rate = 5% or 0.05 Volatility = 20% or 0.20

4. Solution

5. Determinants of Option Pricing/ Variables used in BSM The Strike Price The current stock price The time to expiration The risk-free interest rate The volatility of the stock

6. Current Stock Price (S) Impact on Call Option : The higher the current stock price, the more valuable the call option (the right to buy the stock at the strike price) becomes. If the stock price is above the strike price, the option is more likely to be in-the-money. Impact on Put Option : For put options (the right to sell the stock), a higher stock price decreases the option’s value, as the option becomes less likely to be in-the-money.

7. Strike Price (K) Impact on Call Option : The higher the strike price, the lower the value of the call option, as it becomes less likely that the stock will rise above the strike price by expiration. Impact on Put Option : A higher strike price increases the value of the put option, as it becomes more likely that the stock will fall below the strike price.

8. Time to expiration Impact on Both Call and Put Options : The longer the time to expiration, the higher the option price (for both calls and puts). This is because with more time, there is a greater chance for the stock price to move favorably. Options with longer maturities have more “time value,” which is the part of the option's price not related to intrinsic value.

9. Volatility ( σ) Impact on Both Call and Put Options : Higher volatility increases the price of both call and put options. Volatility represents the uncertainty of the stock’s future price movement. A more volatile stock has a greater chance of making large price moves, which increases the likelihood of the option being in-the-money.

10. Risk-Free Interest Rate (r) Impact on Call Option : As the risk-free interest rate increases, call option prices tend to rise. This is because the present value of the strike price decreases, making it cheaper to buy the stock in the future. Impact on Put Option : Put options tend to decrease in value as interest rates rise. This is because a higher interest rate reduces the present value of cash flows, making it less advantageous to hold a put option.