Question

# Three put options on a stock have the same expiration date and strike prices of \$55,...

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 butterfly spread is synthesized by going long the put with strike \$55, shorting two puts with strike \$60 and going long the put with strike \$65.  If at maturity the price  of the stock is such that , then the payoff of the butterfly is given by:

A) S - 56

B) 64 - S

C) 65 - S

D) S - 55

Calculation of Butterfly payoff at different spot prices :

• On long put we need to pay the premium for purchasing the option.
• On short put we are going to receive the premium for selling the option.
 Spot Price S.No. Particulars 55 60 65 a. Premium paid for long put @ 55 -3 -3 -3 b. Premium received for shorting 2 puts @ 60 (2*5) 10 10 10 c. Premium paid for long put @ 65 -8 -8 -8 d. Value for long put @ 55 on expiry 0 0 0 e. Value for shorting 2 puts @ 60 on expiry -10 0 0 f. Value for long put @ 65 on expiry 10 5 0 g. Pay Off -1 4 -1

So, when the spot will be at \$55 or less it results into a loss; similarly when it is at \$65 or more it results into a loss. It means the butterfly pays between \$56-\$64.

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