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.