A Risk Sensitive Contract-unified Reinforcement Learning Approach for Option Hedging

Paper: arXiv 2411.09659

Authors: Xianhua Peng, Xiang Zhou, Bo Xiao, Yi Wu

Abstract

We propose a new risk sensitive reinforcement learning approach for the dynamic hedging of options. The approach focuses on the minimization of the tail risk of the final P&L of the seller of an option. Different from most existing reinforcement learning approaches that require a parametric model of the underlying asset, our approach can learn the optimal hedging strategy directly from the historical market data without specifying a parametric model; in addition, the learned optimal hedging strategy is contract-unified, i.e., it applies to different options contracts with different initial underlying prices, strike prices, and maturities. Our approach extends existing reinforcement learning methods by learning the tail risk measures of the final hedging P&L and the optimal hedging strategy at the same time. We carry out comprehensive empirical study to show that, in the out-of-sample tests, the proposed reinforcement learning hedging strategy can obtain statistically significantly lower tail risk and higher mean of the final P&L than delta hedging methods.

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 8.5/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper introduces an innovative contract-unified reinforcement learning (CU-RL) framework that overcomes key limitations of traditional deep hedging by optimizing static tail risk (CVaR) across diverse option contracts without needing a parametric model. It combines strong mathematical foundations in risk-sensitive reinforcement learning with robust empirical testing across Black-Scholes, GARCH simulations, and real market data.

Research Flowchart

  flowchart TD
    A[Goal: Model-Free Option Hedging to Minimize Tail Risk] --> B[Input: Historical Market Data & Multiple Option Contracts]
    B --> C[Method: Risk-Sensitive Contract-Unified Deep RL]
    C --> D[Process: Joint Learning of Tail Risk Measure & Optimal Hedging Strategy]
    D --> E[Evaluation: Out-of-Sample Empirical Testing vs Delta Hedging]
    E --> F[Outcomes: Statistically Lower Tail Risk & Higher Mean Final P&L]