Multi-asset market making under the quadratic rough Heston

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.