Smile dynamics IV
Lorenzo Bergomi addresses the relationship between the smile that stochastic volatility models produce and the dynamics they generate for implied volatilities. He introduces a new quantity, the skew stickiness ratio (SSR), and shows 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. He then focuses on short-maturity skews and shows that the difference between realised and implied SSR can be materialised as the profit and loss of an option strategy
In previous work (Bergomi, 2004, 2005, and 2008), we studied the dynamical properties of popular smile models and proposed a new framework for specifying stochastic volatility models with the objective of controlling some of their dynamical properties such as the term structure of the volatilities of volatilities, the level of short forward skew, and the smile of volatility of volatility.
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