Option market making with hedging-induced market impact

ArXiv ID: 2511.02518 “View on arXiv”

Authors: Paulin Aubert, Etienne Chevalier, Vathana Ly Vath

Abstract

This paper develops a model for option market making in which the hedging activity of the market maker generates price impact on the underlying asset. The option order flow is modeled by Cox processes, with intensities depending on the state of the underlying and on the market maker’s quoted prices. The resulting dynamics combine stochastic option demand with both permanent and transient impact on the underlying, leading to a coupled evolution of inventory and price. We first study market manipulation and arbitrage phenomena that may arise from the feedback between option trading and underlying impact. We then establish the well-posedness of the mixed control problem, which involves continuous quoting decisions and impulsive hedging actions. Finally, we implement a numerical method based on policy optimization to approximate optimal strategies and illustrate the interplay between option market liquidity, inventory risk, and underlying impact.

Keywords: Market making, Price impact, Optimal control, Inventory management, Cox processes, Options

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced stochastic control, Cox processes, and rigorous analysis of market impact and arbitrage, indicating high mathematical complexity. It also presents a numerical method based on policy optimization and discusses simulation-based experiments, demonstrating substantial empirical implementation efforts.

  flowchart TD
    Start["Research Goal<br/>Model Option Market Making with<br/>Hedging-Induced Market Impact"] --> Input

    subgraph Input ["Data & Inputs"]
        I1["Stochastic Option Demand<br/>Cox Process Intensities"]
        I2["Underlying Asset State<br/>Inventory & Price Dynamics"]
    end

    Input --> Method

    subgraph Method ["Methodology Steps"]
        M1["Formulate Mixed Control Problem<br/>Continuous Quoting + Impulsive Hedging"]
        M2["Identify Arbitrage &<br/>Market Manipulation Phenomena"]
        M3["Implement Numerical Optimization<br/>Policy Iteration Algorithm"]
    end

    Method --> Outcome

    subgraph Outcome ["Key Findings & Outcomes"]
        F1["Established Well-Posedness<br/>of Control Problem"]
        F2["Optimal Strategies Reveal<br/>Trade-offs: Liquidity vs. Inventory Risk"]
    end

    Start ~~~ Input
    Input ~~~ Method
    Method ~~~ Outcome