  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.
