8. Three month European put options with strike prices of $50, $55, and $60 cost

Question

8. Three month European put options with strike prices of $50, $55, and $60 cost $2, $4, and $7, respectively. A butterfly spread is created by buying a 50-strike put, selling two 55-strike put, and buying a 60-strike put. The risk-free 3-month interest rate is 5%. (a) What is the maximum gain when a butterfly spread is created from the put options? (b) What is the maximum loss when a butterfly spread is created from the put options? (c) For what two values of Sr does the holder of the butterfly spread breakeven, where ST is the stock price in three months?

Explanation / Answer

Ans a) at stock price of $55 investors will have maximum gain.

gain = - put option buy price at $50 + 2* put option buy price at $55 - put option buy price at $60 + payoff from strategy

= - 2$ + 2*4$ - 7$ + max(0,60-55)

= $4

Ans b) He will have maximum loss = put option buy price at $50 + 2* put option buy price at $55 - put option buy price at $60

Maximum loss = - 2$ + 2*4$ - 7$

= -1$

Ans c) Break even points are at stock price of $59 and $51.

at $59

profit from put option at strike price $60 will take care of maximum loss.

at $51 profit from put option at strike price of $60 and loss from 2 put option from $55 will take care of maximum loss.

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