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The Effect Of Skew On Index Option Overwriting

During September European equity indices rallied by between 5%, (the FTSE 100) and 14%, (the Dow Jones Euro STOXX) and over the same period three-month at-the-money index implied volatility fell by around 9% to 10%.

The table shows the Euro STOXX's recent move down in skew seems underdone, both relative to other markets and to the second quarter. The graph below shows how the relationship between three-month at-the-money implied volatility and implied volatility skew--measured as the difference between 25-delta put and call implied volatility--from January last year to June bifurcated between July and October.

Skew seems to have remained "sticky" on the Euro STOXX 50 over the last month, and we should expect it to come down faster than on other indices if the markets continue to rally. It then seems natural to ask what the effect of this falling skew should be on the overwriting strategies.

How Much Does The Skew Matter In Index Option Overwriting?

The choice of strike when overwriting is important because of the skew effect: If you set the strike further out of the money, the performance depends more on the skew. The effect, however, is likely to be different for out-of-the-money puts than for out-of-the-money calls. If you set the strike closer to the spot rate, the performance will depend more on the level of volatility than the steepness of the skew.

To measure the impact of skew and level of volatility on the performance of the strategies we have repriced a series of options with at-the-money volatility. We then recalculated the theoretical risk-adjusted performance for each of the strategies with at-the-money volatility.

This allows us to break the alpha into two parts: (1) The level of volatility: We attribute the theoretical risk-adjusted performance based on at-the-money volatilities to the level of volatility.

(2) The skew: We attribute the difference between the theoretical risk-adjusted performance based on at-the-money volatilities and the actual alphas, calculated with the skew, to the skew. The table shows the attribution due to the skew and level of volatility.

Because out-of-the-money calls generally trade at a lower volatility than at-the-money calls, there is a negative contribution to the alpha from the skew. If out-of-the-money calls were trading at the at-the-money volatility, they would trade at a higher volatility and therefore have a higher premium. If you could sell out-of-the-money calls at the at-the-money volatility, you would realize higher premiums and generate a higher alpha. The contribution to the alpha from the level of volatility is between 24 basis points and 32bps across the various strikes. However, the lower implied volatility for out-of-the-money calls means the actual alpha is between 10-13bps lower. In this case, the skew had a negative impact of 10bps to 13bps.

For puts, the result is exactly the opposite of calls. The contribution to alpha due to the level of volatility is marginal (between 1-5bps). The contribution to alpha from the skew, however, is between 9-11bps.

This is because out-of-the-money puts generally trade at a higher volatility than at-the-money puts. Indeed, for the out-of-the-money puts, almost all of the alpha can be attributed to the skew.

Because of the impact on puts and calls this will naturally also impact strangles and straddles. If you sell a strangle or straddle, you sell a call and a put option. Therefore, the gain from the skew for the put is offset by the loss from the skew for the call. Our results indicate that a strangle allows you to gain much more from the level of volatility. It is also far less sensitive to the steepness of the skew.


This week's Learning Curve was written by Massoud Mussavian (pictured), executive director and European head of derivatives and trading research, and Altaf Kassam, associate, at Goldman Sachs in London.

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