Computing the SSR

TL;DR

This paper derives a model-free formula for the skew-stickiness-ratio (SSR), revealing its dependence on the Hurst exponent and forward variance curve, with implications for options trading and market behavior.

Contribution

It provides a new, model-free expression for the SSR in terms of the characteristic function, linking it to the Hurst exponent and forward variance dynamics.

Findings

SSR limit in diffusion models is H+3/2

Explicit formula for SSR in affine forward variance models

SSR behavior depends on the shape of the forward variance curve

Abstract

The skew-stickiness-ratio (SSR), examined in detail by Bergomi in his book, is critically important to options traders, especially market makers. We present a model-free expression for the SSR in terms of the characteristic function. In the diffusion setting, it is well-known that the short-term limit of the SSR is 2; a corollary of our results is that this limit is $H+3/2$ where $H$ is the Hurst exponent of the volatility process. The general formula for the SSR simplifies and becomes particularly tractable in the affine forward variance case. We explain the qualitative behavior of the SSR with respect to the shape of the forward variance curve, and thus also path-dependence of the SSR.