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 $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, 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.