EX-DRL: Hedging Against Heavy Losses with EXtreme Distributional Reinforcement Learning

ArXiv ID: 2408.12446 “View on arXiv”

Authors: Unknown

Abstract

Recent advancements in Distributional Reinforcement Learning (DRL) for modeling loss distributions have shown promise in developing hedging strategies in derivatives markets. A common approach in DRL involves learning the quantiles of loss distributions at specified levels using Quantile Regression (QR). This method is particularly effective in option hedging due to its direct quantile-based risk assessment, such as Value at Risk (VaR) and Conditional Value at Risk (CVaR). However, these risk measures depend on the accurate estimation of extreme quantiles in the loss distribution’s tail, which can be imprecise in QR-based DRL due to the rarity and extremity of tail data, as highlighted in the literature. To address this issue, we propose EXtreme DRL (EX-DRL), which enhances extreme quantile prediction by modeling the tail of the loss distribution with a Generalized Pareto Distribution (GPD). This method introduces supplementary data to mitigate the scarcity of extreme quantile observations, thereby improving estimation accuracy through QR. Comprehensive experiments on gamma hedging options demonstrate that EX-DRL improves existing QR-based models by providing more precise estimates of extreme quantiles, thereby improving the computation and reliability of risk metrics for complex financial risk management.

Keywords: Distributional Reinforcement Learning, Generalized Pareto Distribution, Quantile Regression, Extreme Quantiles, Gamma Hedging, Equity Derivatives

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematics, including Distributional RL, Quantile Regression, and Generalized Pareto Distributions, with detailed derivations, while demonstrating empirical rigor through comprehensive experiments on gamma hedging options and the release of code.

  flowchart TD
    A["Research Goal: Improve extreme<br>quantile estimation for<br>distributional RL hedging"] --> B["EX-DRL Methodology:<br>Model loss tail with GPD"]
    B --> C{"Data/Inputs:<br>Historical options market data"}
    C --> D["Computation:<br>Integrate GPD tail into<br>Quantile Regression Network"]
    D --> E["Gamma Hedging Experiments<br>on Equity Derivatives"]
    E --> F["Key Outcomes:<br>1. Higher precision for extreme quantiles<br>2. Improved VaR/CVaR accuracy<br>3. Robust hedging strategy"]