1. Dr. WONG buys a 9-month American call with a strike price of $95 on a discrete dividend paying stock with current price $100. $1 and $1.5 dividend will be paid in 3 months and 6 months respectively. Suppose the continuously risk-free rate of interest is 6% per annum. (a) Is he rational to exercise the American call option in 3 months? Explain your answer. Suppose the stock prices are modeled with a 3-period binomial tree based on lognormal model. Each period is 3 months. Dividend will be paid after movement of stock price in 3 months and 6 months. (b) Let S(0.5+)be stock price in 6 months after paying $1.5 dividend. Let S(0.5+)u and S(0.5+)d be the stock price in 9 months if S(0.5+)goes up and down in 9 months respectively. If S(0.5+)d