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 :
|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|
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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