Which implied volatility provides the best measure

Authors: Guan Jun Wang Pierre Yourougou Yue Dong Wang

Publish Date: 2009/11/26

Volume: 36, Issue: 1, Pages: 93-105

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Abstract

The volatility smile/skew phenomenon makes it unclear which implied volatility provides the best measure of the market volatility expectation over the remaining life of the option Due to the high liquidity of atthemoney option and the low sensitivity of its implied volatility to the price error the atthemoney implied volatility is often considered a good measure of future volatility In this paper we raise the question is atthemoney implied volatility the best we can do We provide in this paper an analytical rationale that the implied volatility from option with highest vega outperforms the atthemoney implied volatility in terms of forecasting ability especially for long forecasting horizons Our empirical findings are consistent with our theoretical argumentAssume the true volatility of underlying stock is σ σ A is a close approximation of the true volatility If left fracsigma Asigma rightkern15ptkern15ptsqrt 2left fracr dsigma2 + 1 right then the vega of option with strike of overlineoverline X = Seleft r d rightT + fracsigma A2 T2 is greater than the vega of atthemoney option In other words the sensitivity of implied volatility from option with strike of overlineoverline X = Seleft r d rightT + fracsigma A2 T2 to the price error is lower than that of at the money implied volatility

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