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 :
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.
Get Answers For Free
Most questions answered within 1 hours.