SKEW AND IMPLIED LEVERAGE EFFECT: SMILE DYNAMICS REVISITED

Vincent Vargas (), Tung-Lam Dao () and Jean-Philippe Bouchaud ()
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Vincent Vargas: ENS, 45 rue d'Ulm, 75005 Paris, France
Tung-Lam Dao: CFM, 23 rue de l'Université, 75007 Paris, France
Jean-Philippe Bouchaud: CFM, 23 rue de l'Université, 75007 Paris, France;

International Journal of Theoretical and Applied Finance (IJTAF), 2015, vol. 18, issue 04, 1-15

Abstract: We revisit the "Smile Dynamics" problem, which consists in relating the implied leverage (i.e. the correlation of the at-the-money volatility with the returns of the underlying) and the skew of the option smile. The ratio between these two quantities, called "Skew-Stickiness Ratio" (SSR) by Bergomi (2009), saturates to the value 2 for linear models in the limit of small maturities, and converges to 1 for long maturities. We show that for more general, non-linear models (such as the asymmetric GARCH model), Bergomi's result must be modified, and can be larger than 2 for small maturities. The discrepancy comes from the fact that the volatility skew is, in general, different from the skewness of the underlying. We compare our theory with empirical results, using data both from option markets and from the underlying price series, for the S&P 500 and the DAX. We find, among other things, that although both the implied leverage and the skew appear to be too strong on option markets, their ratio is well explained by the theory. We observe that the SSR indeed becomes larger than 2 for small maturities, signalling the presence of non-linear effects.

Keywords: Option pricing; smile dynamics; skewness (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (1)

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DOI: 10.1142/S0219024915500223

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