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.

1. Calculate , , and  for a two step tree
2. Value the option using a two step tree.
3. Verify that DerivaGem gives the same answer

Use DerivaGem to value the option with 5, 50, 100, and 500 time steps.