8. Suppose that the stock in Figure 2.3 will pay a dividend of 5% of its value at time 2. As before, interest rates are zero and between times 2 and 3 the value of the stock will either increase or decrease by 20. Find the time zero price of an American call option on this stock with strike 100 and maturity 3. Is it ever optimal to exercise early ?

2.3 The tree of stock prices for the underlying stock in Example 2.1.2. The number in brackets is the value of the claim at each node