Moment Explosions in the Rough Heston Model

TL;DR

This paper investigates the conditions under which moments explode in the rough Heston model, establishing their finiteness criteria, bounds, and providing an algorithm for computation, with implications for all maturities and correlations.

Contribution

It demonstrates that moment explosion times in the rough Heston model are finite iff they are finite in the classical Heston model and offers a new algorithm to compute these times.

Findings

Moment explosion time is finite iff for the classical Heston model.

Established bounds for the explosion time.

Developed an algorithm to compute explosion times.

Abstract

We show that the moment explosion time in the rough Heston model [El Euch, Rosenbaum 2016, arxiv:1609.02108] is finite if and only if it is finite for the classical Heston model. Upper and lower bounds for the explosion time are established, as well as an algorithm to compute the explosion time (under some restrictions). We show that the critical moments are finite for all maturities. For negative correlation, we apply our algorithm for the moment explosion time to compute the lower critical moment.