The Zumbach Effect Under Rough Heston

Quantitative Finance, Vol. 20, No. 2, 235-241, 2020.

14 Pages Posted: 24 Sep 2018 Last revised: 9 Jan 2020

See all articles by Omar El Euch

Omar El Euch

Ecole Polytechnique, Paris

Jim Gatheral

CUNY Baruch College

Rados Radoicic

CUNY Baruch College

Mathieu Rosenbaum

Ecole Polytechnique, Palaiseau

Date Written: September 6, 2018

Abstract

Previous literature has identified an effect, dubbed the Zumbach effect, that is nonzero empirically but conjectured to be zero in any conventional stochastic volatility model. Essentially this effect corresponds to the property that past squared returns forecast future volatilities better than past volatilities forecast future squared returns. We provide explicit computations of the Zumbach effect under rough Heston and show that they are consistent with empirical estimates. In agreement with previous conjectures however, the Zumbach effect is found to be negligible in the classical Heston model.

Keywords: Zumbach Effect, Rough Heston Model

JEL Classification: C5, C56

Suggested Citation

El Euch, Omar and Gatheral, Jim and Radoicic, Rados and Rosenbaum, Mathieu, The Zumbach Effect Under Rough Heston (September 6, 2018). Quantitative Finance, Vol. 20, No. 2, 235-241, 2020., Available at SSRN: https://ssrn.com/abstract=3245308 or http://dx.doi.org/10.2139/ssrn.3245308

Omar El Euch

Ecole Polytechnique, Paris ( email )

1 rue Descartes
Paris, 75005
France

Jim Gatheral (Contact Author)

CUNY Baruch College ( email )

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

Rados Radoicic

CUNY Baruch College ( email )

One Bernard Baruch Way
New York, NY 10010
United States

Mathieu Rosenbaum

Ecole Polytechnique, Palaiseau ( email )

Route de Saclay
Palaiseau, 91128
France

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