Repeat Problem for an American put option on a futures contract. The strike price and the futures price are $50. the risk-free rate is 10%, the time to maturity is 6 months, and the volatility is 40% per annum. Consider a European call option on a non-dividend-paying stock where the stock price is S40, 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. d. and p for a two-step tree. (b) Value the option using a two-step tree. (c) Verify that DerivaGem gives the same answer. (d) Use DerivaGem to value the option with 5, 50, 100. and 500 time steps.