A stock price is USD 50 with a volatility of 22%. Assume that the strike price is USD 50, the time to maturity is nine months and the risk-free rate is 3%.

Use the Black-Scholes-Merton formula to value:

a. A European call option

b. A European put option

c. Verify that put-call parity holds 2.

Use risk-neutral valuation to value a derivative that pays off ln() at time , where is the price of a non-dividend paying stock at time .