4. (20 marks) stock price has a expected return of 12% per annum and a volatility of 25% per annum. Currently the s month Europ six tock price is $50. The risk-free interest rate if 5% per annum. consider a put option with a strike price of $34 The time to maturity is 6 months (Gia. 0.5 years). (5 marks) (a) What is the lower bound of the put option? (5 marks) (b) Calculate u, d and p for a one-step tree. (5 marks) c) Value the option using a one-step tree. (5 marks) (d) What is the distribution of the stock price at the option maturity