Consider a European put option on a non-dividend paying stock where the stock price is $40, the strike price is $40, the risk-free rate is 4% per annum, the volatility is 30% per annum, and the time to maturity is 6 months. (a) Calculate u and d according to the Cox-Ross-Rubinstein rule for a single period bino- mial model. Assume that the return from time 0 to 6 months and the return from 6 month to a year are independent and identically distributed. (b) Calculate the risk-neutral probability p for a jump up in the stock price over a period of 6 months. (c) Write a computer code that computes the put option price using an N-period binomial model. Plot your option price as a function of N for N [1,500]. (d) What value do your computed prices converge to?