Question

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.)

Answer 1

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: