3. Three-month European put options with strike prices of $50, $55, and $60 cost $2, $4, and $7, respectively. 1) How can one create butterfly spread...

3. Three-month European put options with strike prices of $50, $55, and $60 cost $2, $4, and $7, respectively.

1) How can one create butterfly spread using these options?

2) Please draw the payoff and profit diagrams of this butterfly strategy.

3) What are the maximum gain and maximum loss of the butterfly spread created using these put options?

4) For which two values of ST does the holder of the butterfly spread break even (with a profit of zero), where ST is the stock price in three months?

5) If you use call options to create butterfly spread that has the same payoff structure as this one, what would be the upfront cost? Why? (Hint: for 3) and 4), the easiest way to proceed is to work with the profit diagram. You can start with the payoff to the holder ignoring the initial cost, and then subtract the net initial cost from the payoff to get the profit.)