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Statistikk › Opsjoner, shorts og posisjonering › Index against stock skew

The index skew is four times steeper than the average single stock skew

MålIndeksAverage single stock
Skew slope, all out of the money options-4.42-1.02
Skew slope, out of the money puts only-5.00-2.04
At the money implied volatilityabout 14%about 26%
Implied volatility on a 10 per cent out of the money putabout 22%about 29%
Risk neutral skewness-1.09-0.53 to -0.17 across named stocks
Weeks with a negative slope100%71% at the lowest

Regression of log implied volatility on log moneyness, short dated options, January 1991 to December 1995 across 1,258 business days on 358,851 out of the money quotes. The paper states the index against stock slope gap is almost seven standard deviations. These figures come from the longer unedited working version; the published version may differ.

Regressing log implied volatility on log moneyness gives a slope of minus 4.42 for the index and minus 1.02 averaged across its thirty largest constituents. The index trades at lower implied volatility and a far steeper smile.

-4.42Index skew slope
-1.02Average across 30 constituent stocks
-5.00Index slope, out of the money puts only
-2.04The same for stocks

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