The Zumbach effect under rough Heston

TL;DR

This paper investigates the Zumbach effect within the rough Heston model, demonstrating that it aligns with empirical data and is negligible in the classical Heston model, highlighting the importance of rough volatility in capturing this phenomenon.

Contribution

It provides explicit calculations of the Zumbach effect under rough Heston, confirming its significance and consistency with empirical observations.

Findings

Zumbach effect is significant in rough Heston model

Effect is negligible in classical Heston model

Empirical estimates align with rough Heston computations

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.