An Offline Learning Approach to Propagator Models

ArXiv ID: 2309.02994 “View on arXiv”

Authors: Unknown

Abstract

We consider an offline learning problem for an agent who first estimates an unknown price impact kernel from a static dataset, and then designs strategies to liquidate a risky asset while creating transient price impact. We propose a novel approach for a nonparametric estimation of the propagator from a dataset containing correlated price trajectories, trading signals and metaorders. We quantify the accuracy of the estimated propagator using a metric which depends explicitly on the dataset. We show that a trader who tries to minimise her execution costs by using a greedy strategy purely based on the estimated propagator will encounter suboptimality due to so-called spurious correlation between the trading strategy and the estimator and due to intrinsic uncertainty resulting from a biased cost functional. By adopting an offline reinforcement learning approach, we introduce a pessimistic loss functional taking the uncertainty of the estimated propagator into account, with an optimiser which eliminates the spurious correlation, and derive an asymptotically optimal bound on the execution costs even without precise information on the true propagator. Numerical experiments are included to demonstrate the effectiveness of the proposed propagator estimator and the pessimistic trading strategy.

Keywords: Price impact kernel, Offline reinforcement learning, Propagator model, Pessimistic loss functional, Liquidation strategy, Equities

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats
• Why: The paper presents highly advanced mathematical frameworks including stochastic control, Volterra equations, nonparametric estimation, and regret analysis with heavy derivations and theoretical proofs. Empirical validation is limited to included numerical experiments demonstrating effectiveness, but lacks real-world data backtesting or code implementation details.

  flowchart TD
    Start(["Research Goal"]) -->|Estimate Price Impact Kernel & Design Optimal Liquidation Strategy| Inputs["Data/Inputs<br/>Static Dataset<br/>- Correlated Price Trajectories<br/>- Trading Signals<br/>- Metaorders"]
    
    Inputs -->|Nonparametric Estimation| Method1["Key Methodology<br/>Propagator Estimator<br/>Quantifies Accuracy vs Dataset"]
    Method1 -->|Quantifies Bias & Uncertainty| Prob["Identify Suboptimality Causes<br/>1. Spurious Correlation<br/>2. Biased Cost Functional"]
    
    Prob -->|Offline RL Approach| Method2["Key Methodology<br/>Pessimistic Loss Functional<br/>Optimiser removes Spurious Correlation"]
    Method2 -->|Computational Process| Comp["Optimisation<br/>Minimise Execution Costs<br/>Account for Uncertainty"]
    
    Comp --> Outcomes["Key Findings/Outcomes<br/>1. Accurate Propagator Estimation<br/>2. Asymptotically Optimal Bound<br/>3. Pessimistic Strategy outperforms Greedy"]
    
    Start -->|Strategies to liquidate risky asset| Outcomes