Question 4 (25 points) A (European-type) gap call option has the payoff (S(T) K1)1(S(T) > K2). That is, the payoff is (S(T) K1) if S(T) > K2, and 0 otherwise.

Here K1 is the strike price, i.e. , the amount paid for the stock if the option is exercised.

K2 is the trigger price, i.e., the price that determines if the option is exercised (in other words, the exercise on a gap option is non-elective. If the trigger condition is met, the option must be exercised. In particular, negative payoff can occur. ) Consider the two-period binomial model : t {0, 1}. You are given u = 1.2 and d = 0.9. The periodic continuously compounded risk-free rate is r = 0.04. There is no dividend. Assume that the initial risky asset price is S0 = 100. What is the unique time-0 price of a gap call option with K1 = 100 and K2 = 95 ? What is the replicating portfolio ?