Consider a European call option on a non-dividend paying stock where the stock price is $40, the strike price is $40, the risk-free rate is 8% per annum, the volatility is 30% per annum and the time to maturity is 6-months. (a) Construct a two-step binomial tree, calculating u and d using the Cox-Ross- Rubinstein approach to matching volatility. (b) Show that the call price is $3.772, using a two-step tree. (c) Compute the prices of American and European puts, both with the same strike price and time to maturity as the European call, again using a two-step tree.