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Smile dynamics -- a theory of the implied leverage effect

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  • Stefano Ciliberti

    (CFM)

  • Jean-Philippe Bouchaud

    (CFM)

  • Marc Potters

    (CFM)

Abstract

We study in details the skew of stock option smiles, which is induced by the so-called leverage effect on the underlying -- i.e. the correlation between past returns and future square returns. This naturally explains the anomalous dependence of the skew as a function of maturity of the option. The market cap dependence of the leverage effect is analyzed using a one-factor model. We show how this leverage correlation gives rise to a non-trivial smile dynamics, which turns out to be intermediate between the "sticky strike" and the "sticky delta" rules. Finally, we compare our result with stock option data, and find that option markets overestimate the leverage effect by a large factor, in particular for long dated options.

Suggested Citation

  • Stefano Ciliberti & Jean-Philippe Bouchaud & Marc Potters, 2008. "Smile dynamics -- a theory of the implied leverage effect," Papers 0809.3375, arXiv.org.
    • Handle: RePEc:arx:papers:0809.3375
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    File URL: http://arxiv.org/pdf/0809.3375
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    Cited by:

    1. Itkin, Andrey, 2015. "To sigmoid-based functional description of the volatility smile," The North American Journal of Economics and Finance, Elsevier, vol. 31(C), pages 264-291.
    2. Florent S'egonne, 2015. "Variance Dynamics - An empirical journey," Papers 1507.00846, arXiv.org.

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