Assume the Black-Scholes framework. Consider a non-dividend paying stock with the current price 0.

You are given the following: The expiry date is T. The continuously compounded risk-free interest rate is r per annum. The strike price of the option is K. a) Use put-call parity to derive the Black-Scholes analytical formula for a European put option on this stock. [4] b) Consider a 1-year at-the-money European call option on this stock with the current price 0 = 100 and volatility 40% per annum. The continuously compounded rate of interest is r = 2% per annum.

i. Use the Black-Scholes model to compute the price of the call option. ii. Compute the delta of this call option iii. Use put-call parity to compute the price of the corresponding European put option with the same maturity and same strike price. iv. Compute the delta of this put option.