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.