Consider a European call option on a non dividend paying stock when the stock pr

Question

Consider a European call option on a non dividend paying stock when the stock price is $25.00, the strike price is $28.00, the risk-free interest rate is 8% per annum, the volatility is 30% per annum and there is four years to maturity.

a) Find the current price of the option. Show your calculations. Now assume the stock price instantaneously changes to $25.50.

b) Use the delta of the option to estimate the value of the option after the change. Show your calculations.

c) Use the delta and gamma of the option to estimate the value of the option after the change. Show your calculations.

d) What is the exact value of the option after the change? Show your calculations.

Explanation / Answer

1.a) First arrive d1 and d2 for black-scholes model using the given information below.

value under orignal circumstances.

A.) Value after changes

There is no substaintial change.

b) Gamma will be as follows:

d.) Value of option only changes by fractions as black scholes model shows.

A Natural log of stock price/strike price -0.11333 Natural log of stock price/strike price -0.11333 B Risk-free rate+(Volatility^2/2) 0.41 Risk-free rate-(Volatility^2/2) 0.23 C A+B 0.29667 A+B 0.11667 D Volatility*square-root of time to maturity 0.6 Volatility*square-root of time to maturity 0.6 E d1=C/D 0.49445 d2=C/D 0.19445

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