Multi-asset market making under the quadratic rough Heston

TL;DR

This paper develops a multi-asset market making strategy under the quadratic rough Heston model, providing an asymptotic solution that balances profit maximization with inventory risk control in a high-dimensional setting.

Contribution

It introduces a novel multi-asset market making framework using the quadratic rough Heston model and derives an asymptotic closed-form solution for the complex optimization problem.

Findings

The asymptotic solution effectively balances profit and risk.

Numerical experiments validate the accuracy of the approximations.

The approach handles high-dimensional optimization efficiently.

Abstract

Given the promising results on joint modeling of SPX/VIX smiles of the recently introduced quadratic rough Heston model, we consider a multi-asset market making problem on SPX and its derivatives, e.g. VIX futures, SPX and VIX options. The market maker tries to maximize its profit from spread capturing while controlling the portfolio's inventory risk, which can be fully explained by the value change of SPX under the particular setting of the quadratic rough Heston model. The high dimensionality of the resulting optimization problem is relaxed by several approximations. An asymptotic closed-form solution can be obtained. The accuracy and relevance of the approximations are illustrated through numerical experiments.