Computing the SSR

22 Pages Posted: 27 Jun 2024

See all articles by Peter Friz

Peter Friz

Technische Universität Berlin (TU Berlin)

Jim Gatheral

CUNY Baruch College

Date Written: June 21, 2024

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 modelfree 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.

Keywords: Skew-stickiness ratio, stochastic volatility, rough volatility, forward variance model, characteristic function, forest expansion

Suggested Citation

Friz, Peter and Gatheral, Jim, Computing the SSR (June 21, 2024). Available at SSRN: https://ssrn.com/abstract=4872776 or http://dx.doi.org/10.2139/ssrn.4872776

Peter Friz

Technische Universität Berlin (TU Berlin) ( email )

Straße des 17
Juni 135
Berlin, 10623
Germany

Jim Gatheral (Contact Author)

CUNY Baruch College ( email )

Department of Mathematics
One Bernard Baruch Way
New York, NY 10010
United States

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