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Suppose option prices for a Dec. 31 expiration and an exercise price of 2300 are Call...

Suppose option prices for a Dec. 31 expiration and an exercise price of 2300 are Call = 586 and Put = 386. Option prices for a Dec. 31 expiration and an exercise price of 2700 are Call = 426 and Put = 626.  You believe the market has overestimated volatility in the S&P 500 index. Construct a synthetic ‘short straddle’ in which you will have a profit with small changes in the S&P 500 index and a loss with large changes in the index.  Graph your results in Excel. (Hint: your profit diagram will look like a V.)

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Expert Solution

Short straddle strategy involves a payoff in the shape of an inverted V. We will short the call and the put at the same strike price. If the price currently is near 2300, we can do it with the 2300 strike price or if it is near 2700 currently, we can do it with the 2700 strike price. Suppose we do it for 2300. Below is the payoff table for it.

Strike =2300 Payoff from call Payoff from Put Total
1550 586 -364 222
1600 586 -314 272
1650 586 -264 322
1700 586 -214 372
1750 586 -164 422
1800 586 -114 472
1850 586 -64 522
1900 586 -14 572
1950 586 36 622
2000 586 86 672
2050 586 136 722
2100 586 186 772
2150 586 236 822
2200 586 286 872
2250 586 336 922
2300 586 386 972
2350 536 386 922
2400 486 386 872
2450 436 386 822
2500 386 386 772
2550 336 386 722
2600 286 386 672
2650 236 386 622
2700 186 386 572
2750 136 386 522
2800 86 386 472
2850 36 386 422
2900 -14 386 372
2950 -64 386 322
3000 -114 386 272
3050 -164 386 222
3100 -214 386 172

As we can see from the table, the profit increases for the middle values and decreases at high or low stock prices. The payoff graph will look like:

jeff jeffy answered 1 year ago
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