Consider a three period binomial model (one initial date and two steps) as in class. Let the initial stock price be $100. Let the upward increments be u = 1.2 and the downward be d = .9. Thus, the up-up state should have Suu = u u S0 = 1.2 1.2 100 = 144 and so on. The risk free rate is ten percent per period. The call option with strike price of $100 was priced in class.

a. Price the put option with strike price of $100 using replicating portfolios. Does put-call parity hold (remember the interest accrues in discrete steps)? Explain.

b. Suppose we had an Asian call option whose payoff is max{SK, 0} where S is the average stock price, with strike K = 100. So, if the state is up-up the payoff would be (100 + 120 + 144)/3 100 = 21.33. Use replicating portfolios to price this option.