The price of a security in each time period is its price inthe previous time period multiplied either by u = 1.25 or by d = .8.The initial price of the security is 100. Consider the following exoticEuropean call option that expires after five periods and has a strike price

of 100. What makes this option exotic is that it becomes alive only ifthe price after two periods is strictly less than 100. That is, it becomesalive only if the price decreases in the first two periods. The final payoffof this option is

payoff at time 5 = I(S(5) 100)+,where I = 1 if S(2) < 100 and I = 0 if S(2) 100. Suppose the interestrate per period is r = .1.

(a) What is the no-arbitrage cost (at time 0) of this option?

(b) Is the cost of part (a) unique? Briefly explain.

(c) If each price change is equally likely to be an up or a down movement,what is the expected amount that an option holder receives at

the time of expiration?