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 steps