10.

a. A butterfly spread is the purchase of one call at exercise price X 1 , the sale of two calls at exercise price X 2 , and the purchase of one call at exercise price X 3 . X 1 is less than X 2 , and X 2 is less than X 3 by equal amounts, and all calls have the same expiration date. Graph the payoff diagram to this strategy.

b. A vertical combination is the purchase of a call with exercise price X 2 and a put with exercise price X 1 , with X 2 greater than X 1 . Graph the payoff to this strategy.