Question 18 a) Calculate the price of a European put option on a non-dividend-paying stock when the stock price is $50, the strike price is $48, the risk-free interest rate is 6% per annum, the volatility is 30% per annum, and the time to maturity is six months? (4 marks) b) Show (using mathematical proof) that the Black-Scholes-Merton formulas for European call and put options satisfy the put-call parity condition. (4 marks) (4 4 8 marks) Question 18 a) Calculate the price of a European put option on a non-dividend-paying stock when the stock price is $50, the strike price is $48, the risk-free interest rate is 6% per annum, the volatility is 30% per annum, and the time to maturity is six months? (4 marks) b) Show (using mathematical proof) that the Black-Scholes-Merton formulas for European call and put options satisfy the put-call parity condition. (4 marks) (4 4 8 marks)