A generalization of the rational rough Heston approximation

Abstract

Previously, in Gatheral and Radoičić (Rational approximation of the rough Heston solution. Int. J. Theor. Appl. Finance, 2019, 22(3), 1950010), we derived a rational approximation of the solution of the rough Heston fractional ODE in the special case $\lambda =0$, which corresponds to a pure power-law kernel. In this paper we extend this solution to the general case of the Mittag-Leffler kernel with $\lambda \ge 0$. We provide numerical evidence of the convergence of the solution.

Keywords:

• Rough Heston model
• Padé approximant
• Rational approximation
• Volatility smile
• Mittag-Leffler

JEL Classifications:

• C30
• C20
• C40
• C60

Open Scholarship

This article has earned the Center for Open Science badges for Open Data and Open Materials through Open Practices Disclosure. The data and materials are openly accessible at https://github.com/ jgatheral/RationalRoughHeston .

Acknowledgments

We are grateful to Giacomo Bormetti and his collaborators for sharing their efficient Adams scheme code and to Stefano Marmi for enlightening conversations.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 More precisely in the limit $H\downarrow 0$ in the sense of Forde et al. (2021).