Consider a European call option on a non dividend paying stock when the stock price is $35.00, the exercise price is $42.00, the continuously compounded risk-free interest rate is 6% per annum, the volatility is 28% per annum and there is four years to maturity.

(a) Find the current price of the option. Show your calculations. (6marks)

(b) Use the delta of the option to estimate the value of the option after the change. Show your calculations. (1 mark)

(c) Use the delta and gamma of the option to estimate the value of the option after the charge. Show your calculations. (3 marks)

(d) Why is the option value you found in part(c) is different from the one you found in part(b)? (1 mark)