The price of Apple is $197 today. Its annualized volatility in the past year is 20%. Consider a call option expiring in 6 months with strike price K=195. Assume the interest rate is 0.

1. (1) In a one-period binomial tree model, calculate the risk neutral probability q, parameters u

   and d. Recall that u = e and d = e, where is the annualized volatility and T is

   period in years.

2. (2) Calculate the price of the call option in this one-period model

3. (3) Calculate the price of the call option in a two-period model (note that in this case, T is 3

   months instead of 6 months, so you have to re-calculate q, u and d)

4. (4) Extra credit: using computer programs or by hand, compute the option price under a 5-

   period binomial tree model (5pts, and the total score on this problem set cannot exceed 100)