( 25 points) 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=60 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 is r=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 70 . 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." (iv) Find date-0 price of European put option on the risky asset with the same expiration date and exercise price as the call option in part (ii) using the putcall parity relationship