Assignment: Consider a European call option on a non-dividend-paying stock where the stock price is $50, the strike price is $50, the risk-free rate is 5% per annum, the volatility is 35% 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 what is the length of each time step? This is the value for delta t. Use this value for your calculations.
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. What happens to the calculated price as the time steps are increased (delta t decreases)?