Consider a binomial model with three dates t = 0, 1, 2, two events up and down at date 1, and two date-2 successors (up and down) of each date-1 event. The price of the risky asset is S0 = 50 at date 0 and moves up by factor u = 1.3 or down by factor d = 1 each period. One-period risk-free rate of return isr = 0.2, the same at dates 1 and 2.

(i) Find strictly positive state prices and risk-neutral probabilities.

(ii) Find date-0 price of European call option on the risky asset with expiration date 2 and exercise price 60. Find date 1 prices of the option in events up

and down.

(iii) Suppose that the call option is American so that it can be exercised at date

1. Is it better to exercise the option or sell it at date 1 in event up? Do the same comparison for event down. Would the price of the American option at date 0 be different from the price of the European option? Explain.