Repeat Problem 13.25 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 six months, and the volatility is 40% per annum.

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.