Problem 2. (Prob. 1 continued) We consider the same stock evolution as in Problem 1, but we now assume that the market is 3-period and the expiration date of the options is T = 3 years. (a) Repeat questions (a), (b) and (c) of Problem 1 in this new market. (You don't have to provide all the calculations, numerical results are sufficient.) (b) We consider a new type of option on this market: an American straddle option with strike price K = 5. The payoff of an American straddle is the sum of the payoffs of an American call and an American put. If you exercise it when St = 6, your payoff is 1. If you exercise it when S1 = 2, your payoff is 3. You are allowed to exercise at any time. Find the price of this option. (c) Describe the optimal exercising strategy. 1 (d) Let Co (resp. Po, Ko) be the prices of the American call (resp. put, straddle). Give an intuitive explanation why you found that Ko < Co + Po.

Please solving problem2

Problem1

We consider a two-period binomial model with the following properties: each period lasts
one (1) year and the current stock price is S0 = 4. On each period, the stock price doubles
when it moves up and is reduced by half when it moves down. The annual interest rate
on the money market is 25%. (This model is the same as in Prob. 1 of HW#2).
We consider four options on this market:
ˆ A European call option with maturity T = 2 years and strike price K = 5;
ˆ A European put option with maturity T = 2 years and strike price K = 5;
ˆ An American call option with maturity T = 2 years and strike price K = 5;
ˆ An American put option with maturity T = 2 years and strike price K = 5.
(a) Find the price at time 0 of both European options.
(b) Find the price at time 0 of both American options. Compare your results with (a)
and comment.
(c) For each of the American options, describe the optimal exercising strategy.