The Quadratic Rough Heston Model and the Joint S&P 500/VIX Smile Calibration Problem

11 Pages Posted: 31 Jan 2020

See all articles by Jim Gatheral

Jim Gatheral

CUNY Baruch College

Paul Jusselin

Ecole Polytechnique, Palaiseau

Mathieu Rosenbaum

Ecole Polytechnique, Palaiseau

Date Written: January 6, 2020

Abstract

Fitting simultaneously SPX and VIX smiles is known to be one of the most challenging problems in volatility modeling. A long-standing conjecture due to Julien Guyon is that it may not be possible to calibrate jointly these two quantities with a model with continuous sample-paths. We present the quadratic rough Heston model as a counterexample to this conjecture. The key idea is the combination of rough volatility together with a price-feedback (Zumbach) effect.

Keywords: SPX smiles, VIX smiles, rough Heston model, Zumbach effect, quadratic rough Heston model, Guyon's conjecture

JEL Classification: G13

Suggested Citation

Gatheral, Jim and Jusselin, Paul and Rosenbaum, Mathieu, The Quadratic Rough Heston Model and the Joint S&P 500/VIX Smile Calibration Problem (January 6, 2020). Available at SSRN: https://ssrn.com/abstract=3514894 or http://dx.doi.org/10.2139/ssrn.3514894

Jim Gatheral

CUNY Baruch College ( email )

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

Paul Jusselin (Contact Author)

Ecole Polytechnique, Palaiseau ( email )

Palaiseau
France

Mathieu Rosenbaum

Ecole Polytechnique, Palaiseau ( email )

Route de Saclay
Palaiseau, 91128
France

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