Paper: arXiv 2609.26606

Authors: Samuel N. Cohen, Lyndon Drake, Zihan Guo, Christoph Reisinger

Abstract

We provide a model for the nested optimisation problem of market making and rebate design problems in option markets and find optimal strategies. A single market maker trades multiple European call options in a local-stochastic volatility option market with both make and take strategies, modeled, respectively, as continuous and impulse controls. Her objective is to maximize, over all admissible make-take strategies, net profit of option portfolio value and cumulative rebate revenue, subject to a penalty on residual portfolio delta and vega. In addition, we demonstrate how an exchange can incentivize a market maker to improve market liquidity by setting suitable fee rebates, thereby resolving its own liquidity attraction problem. To this end, we propose a three-step rebate design scheme with flexibility to accommodate specific liquidity targets imposed by an exchange. Numerical results are provided to validate the effectiveness of the proposed scheme.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper presents a highly mathematical model for market making and rebate design in option markets, incorporating advanced stochastic control and optimization techniques. It demonstrates strong empirical validation through numerical results using real option order book data, showcasing both theoretical depth and practical application. The novelty lies in its integrated approach to inventory management and exchange-side liquidity attraction within a local-stochastic volatility framework.

Research Flowchart

  flowchart TD
    A[Research Goal: Optimize Liquidity Provision & Rebate Design] --> B{Methodology: Nested Optimization Problem};
    B --> C[Model: Single MM, Multiple European Call Options, Local-Stochastic Volatility];
    C --> D{Inputs: Make-Take Strategies, Option Portfolio Value, Rebate Revenue, Delta/Vega Penalty};
    D --> E[Computation: Solve Optimal Strategies, Rebate Design Scheme (3-Step)];
    E --> F{Outcomes: Optimal MM Strategies, Incentive-Compatible Rebate Design, Improved Market Liquidity};
    F --> G[Validation: Numerical Results Confirm Effectiveness].