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 six 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.