15. A European shout option is an option for which the payoff at expiration is max(0, S − K, G − K), where G is the price at which you shouted. (Suppose you have an XYZ shout call with a strike price of $100. Today XYZ is $130. If you shout at $130, you are guaranteed a payoff of max($30, ST

− $130) at expiration.) You can only shout once, irrevocably.

a. Demonstrate that shouting at some arbitrary priceG>K is better than never shouting.

b. Compare qualitatively the value of a shout option to (i) a lookback option

(which pays max[0, ST

− K], where ST is the greatest stock price over the life of the option) and (ii) a ladder option (which pays max(0, S − K, L − K)

if the underlying hits the value L at some point over the life of the option).

c. Explain how to value this option binomially. (Hint: Think about how you would compute the value of the option at the moment you shout.)