A butterfly spread can be created using put options by buying a put option with a relatively low exercise price, K1, buy a put option with relatively high exercise price, K3, and sell two put options with an exercise price, K2, halfway between K1 and K3. All options are on the same stock and have the same expiration date.

European put options on a stock with exercise (strike) prices $100, $105, and $110 with a maturity of six months cost $2.62, $4.41, and $6.80, respectively. Construct a butterfly spread using the three put options. Ignore time value of money, transaction costs, and taxes.

a) Find the initial cash flow from the creation of the butterfly spread. b) Complete the table below that shows the payoffs and profits (or losses) of the butterfly spread. ST stands for the stock price at the expiration date. Assume that options are exercised if they are in-the-money and are not exercised if they are at-the-money or out-of-the-money at expiration. Show your calculations.

Stock price range at option expiration date Payoff Profit

S < $100

100 S < 105

105 S < 110

S 110