Mean-reversion Properties of Implied Volatilities

35 Pages Posted: 16 Oct 2007 Last revised: 24 Jul 2010

See all articles by Florian Ielpo

Florian Ielpo

Université Paris I Panthéon-Sorbonne - Centre d'Economie de la Sorbonne (CES); Unigestion

Guillaume Simon

Capital Fund Management

Date Written: July 22, 2010

Abstract

In this paper, we present a new stylized fact for options whose underlying asset is a stock index. Extracting implied volatility time series from call and put options on the DAX and FTSE indexes, we show that the persistence of these volatilities depends on the moneyness of the options used for its computation. Using a functional autoregressive model, we show that this effect is statistically significant. Surprisingly, we show that the diffusion-based stochastic volatility models are not consistent with this stylized fact. Finally, we argue that adding jumps to a diffusion-based volatility model help recovering this volatility pattern. This suggests that the persistence of implied volatilities can be related to the tails of the underlying volatility process: this corroborates the intuition than the liquidity of the options across moneynesses introduces an additional risk factor to the one usually considered.

Keywords: Implied Volatility, Stylized Fact, Stochastic Volatility Models, Volatility

JEL Classification: C32, G13

Suggested Citation

Ielpo, Florian and Simon, Guillaume, Mean-reversion Properties of Implied Volatilities (July 22, 2010). Available at SSRN: https://ssrn.com/abstract=1021560 or http://dx.doi.org/10.2139/ssrn.1021560

Florian Ielpo (Contact Author)

Université Paris I Panthéon-Sorbonne - Centre d'Economie de la Sorbonne (CES) ( email )

106-112 Boulevard de l'hopital
106-112 Boulevard de l'Hôpital
Paris Cedex 13, 75647
France

Unigestion ( email )

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CP 387
Genève 12, CH 1211
Switzerland

Guillaume Simon

Capital Fund Management ( email )

23 rue de l'Université
Paris, 75007
France

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