Three put options on a stock have the same expiration date and strike prices of $55, $60, and $65. The market prices are $3, $5, and $8 respectively.

a. Explain how a butterfly spread can be created from these three options.

b. Construct a table showing the payoff and profit from this strategy for different values of S_T.

c. Sketch the profit as a function of S_T.

d. For what values of S_T does the butterfly spread result in a loss?