Smile Dynamics IV

12 Pages Posted: 13 Dec 2009

Date Written: June 1, 2009

Abstract

In this paper we address the relationship between the smile that stochastic volatility models produce and the dynamics they generate for implied volatilities. We introduce a new quantity, which we call the Skew Stickiness Ratio and show how, at order one in the volatility of volatility, it is linked to the rate at which the at-the-money-forward skew decays with maturity. We then focus on short maturity skews and (a) show that the difference between realized and implied SSR can be materialized as the P&L of an option strategy, (b) introduce the notion of realized skew.

JEL Classification: G13

Suggested Citation

Bergomi, Lorenzo, Smile Dynamics IV (June 1, 2009). Available at SSRN: https://ssrn.com/abstract=1520443 or http://dx.doi.org/10.2139/ssrn.1520443

Lorenzo Bergomi (Contact Author)

Societe Generale ( email )

Paris-La Défense, Paris 92987
France

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