Paper: arXiv 2212.10164

Authors: Mathieu Rosenbaum, Jianfei Zhang

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.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 4.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents high mathematical complexity by extending the quadratic rough Heston framework to a high-dimensional multi-asset market making setting with closed-form asymptotic approximations. However, it relies heavily on numerical simulations rather than extensive empirical backtests on real market data, limiting its immediate empirical rigor.

Research Flowchart

  flowchart TD
    A["Research Goal: Multi-Asset Market Making<br>under Quadratic Rough Heston Model"] --> B["Inputs: SPX & Derivative Prices<br>(VIX Futures, SPX/VIX Options)"]
    B --> C["Formulate Stochastic Control Problem<br>(Maximize Profit vs. Inventory Risk)"]
    C --> D["Apply Dimensionality Reduction<br>& Approximations"]
    D --> E["Derive Asymptotic<br>Closed-Form Solution"]
    E --> F["Perform Numerical Experiments<br>& Validate Model Accuracy"]
    F --> G["Outcome: Efficient Joint SPX/VIX<br>Market Making & Risk Control"]