Optimal Entry and Exit with Signature in Statistical Arbitrage

ArXiv ID: 2309.16008 “View on arXiv”

Authors: Unknown

Abstract

In this paper, we explore an optimal timing strategy for the trading of price spreads exhibiting mean-reverting characteristics. A sequential optimal stopping framework is formulated to analyze the optimal timings for both entering and subsequently liquidating positions, all while considering the impact of transaction costs. Then we leverages a refined signature optimal stopping method to resolve this sequential optimal stopping problem, thereby unveiling the precise entry and exit timings that maximize gains. Our framework operates without any predefined assumptions regarding the dynamics of the underlying mean-reverting spreads, offering adaptability to diverse scenarios. Numerical results are provided to demonstrate its superior performance when comparing with conventional mean reversion trading rules.

Keywords: Optimal Stopping, Mean Reversion, Signature Optimal Stopping, Transaction Costs, Spread Trading, Equities / Derivatives

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematics including optimal stopping theory, signature methods, and Ornstein-Uhlenbeck processes with numerical experiments on real data, though it lacks specific backtesting code or exhaustive data sets.

  flowchart TD
    A["Research Goal<br>Optimal Entry/Exit for<br>Mean-Reverting Spreads"] --> B["Key Inputs & Constraints<br>Price Spread Data & Transaction Costs"]
    B --> C["Core Methodology<br>Sequential Optimal Stopping<br>via Signature Method"]
    C --> D["Computational Process<br>Solve without Predefined<br>Dynamic Assumptions"]
    D --> E["Key Outcome 1<br>Optimal Entry & Exit<br>Timings"]
    D --> F["Key Outcome 2<br>Superior Performance vs.<br>Conventional Rules"]
    E --> G((Final Result<br>Maximized Gains in<br>Spread Trading))
    F --> G