Deep Hedging with Market Impact

ArXiv ID: 2402.13326 “View on arXiv”

Authors: Unknown

Abstract

Dynamic hedging is the practice of periodically transacting financial instruments to offset the risk caused by an investment or a liability. Dynamic hedging optimization can be framed as a sequential decision problem; thus, Reinforcement Learning (RL) models were recently proposed to tackle this task. However, existing RL works for hedging do not consider market impact caused by the finite liquidity of traded instruments. Integrating such feature can be crucial to achieve optimal performance when hedging options on stocks with limited liquidity. In this paper, we propose a novel general market impact dynamic hedging model based on Deep Reinforcement Learning (DRL) that considers several realistic features such as convex market impacts, and impact persistence through time. The optimal policy obtained from the DRL model is analysed using several option hedging simulations and compared to commonly used procedures such as delta hedging. Results show our DRL model behaves better in contexts of low liquidity by, among others: 1) learning the extent to which portfolio rebalancing actions should be dampened or delayed to avoid high costs, 2) factoring in the impact of features not considered by conventional approaches, such as previous hedging errors through the portfolio value, and the underlying asset’s drift (i.e. the magnitude of its expected return).

Keywords: Dynamic Hedging, Deep Reinforcement Learning, Market Impact, Liquidity, Options, Equities

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 4.0/10
• Quadrant: Lab Rats
• Why: The paper heavily employs advanced mathematics, including stochastic control, convex optimization, and deep reinforcement learning theory, with detailed derivations and formalisms. While it uses simulations to compare against delta hedging, there is no mention of real-world backtests, actual limit order book data, or statistical metrics like Sharpe ratios on live data, placing it in the ‘Lab Rats’ quadrant.

  flowchart TD
    A["Research Goal<br>Optimize hedging with<br>market impact using DRL"] --> B{"Methodology"}
    
    B --> C["Data & Inputs"]
    C --> D["Option & Stock Prices<br>Convex Market Impact<br>Liquidity Constraints"]
    
    B --> E["Computational Process"]
    E --> F["Deep Reinforcement Learning<br>Environment: Sequential Trading<br>Action: Hedge Ratio"]
    
    F --> G["Optimization<br>Minimize Costs vs Tracking Error<br>via Reward Function"]
    
    G --> H["Key Findings & Outcomes"]
    H --> I["DRL Model Outperforms<br>Delta Hedging in Low Liquidity"]
    H --> J["Optimal Policy Learned:<br>Dampen/Delay Actions to<br>Avoid High Costs"]
    H --> K["Incorporates Feature Impact:<br>Previous Errors & Asset Drift"]
    
    D --> F
    G --> H