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

Homework Answers

Answer #1

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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