1. A butterfly spread is a combination of option positions that involves three strike prices. To create a butterfly spread, a trader purchases an option with a low strike price and an option with a high strike price, and sells two options with an intermediate strike price. For this problem, assume that the intermediate strike price is halfway between the low and the high strike prices and that the options are European. Denote the intermediate strike price by K, the low strike price by K-a, and the high strike price by K +a, a > 0. (a) Graph the payoff diagram at maturity of the butterfly spread in which the under- lying options are call options. Holding the intermediate strike price fixed, what happens to the payoffs as the low and high strike price converge to the interme- diate price? (b) Suppose that a trader purchases a butterfly spread for which the intermediate strike price is equal to today's stock price. Based only on this trade, what is the trader's view of the future direction of the market? c) Show that the same butterfly spread can be constructed using put options instead of call options. Using put-call parity, show that the initial investment is the same in both cases, i.e. whether you use puts or you use calls to create the spread