Problem
Consider a European call option on a non-dividend-paying stock where the stock price is $60, the strike price is $60, the risk-free rate is 6% per annum, the volatility is 30% per annum, and the time to expiration is six months.
Q1: Calculate u, d, and p for a two-step tree. Hint: if the expiration is six months and there are two steps, then the length of each time step delta t ) is 3 months (=0.25).
Q2: Value the option using a two-step tree.
Q3: Verify that Derivagem gives the same answer (use European Binomial with two steps). Hint: if your response for part Q3 does not match your response from Q2, then at least one of them is incorrect!
Q4: Use Derivagem to value the option with 5, 50, 100, and 500 steps.