An Application of the Ornstein-Uhlenbeck Process to Pairs Trading

ArXiv ID: 2412.12458 “View on arXiv”

Authors: Unknown

Abstract

We conduct a preliminary analysis of a pairs trading strategy using the Ornstein-Uhlenbeck (OU) process to model stock price spreads. We compare this approach to a naive pairs trading strategy that uses a rolling window to calculate mean and standard deviation parameters. Our findings suggest that the OU model captures signals and trends effectively but underperforms the naive model on a risk-return basis, likely due to non-stationary pairs and parameter tuning limitations.

Keywords: Pairs Trading, Ornstein-Uhlenbeck Process, Statistical Arbitrage, Mean Reversion, Stationarity

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 4.0/10
• Quadrant: Lab Rats
• Why: The paper employs advanced stochastic calculus and econometric testing (cointegration, OU process SDEs), but the empirical validation is preliminary, using a limited dataset without robust out-of-sample testing or risk management refinements.

  flowchart TD
    A["Research Goal: Compare OU Process Model vs. Naive Rolling Window<br/>for Pairs Trading Signals"] --> B
    subgraph B ["Methodology & Inputs"]
        direction LR
        B1["Pair Selection<br/>Stock Price Data"] --> B2["Spread Calculation<br/>Price Ratio or Log Spread"]
    end
    B --> C{"Computational Modeling"}
    C --> D["Naive Strategy<br/>Rolling Mean & STD"]
    C --> E["OU Process Strategy<br/>MLE Parameter Estimation"]
    D --> F
    E --> F["Strategy Evaluation<br/>Risk-Return Metrics"]
    F --> G["Findings & Outcomes"]
    subgraph G []
        direction TB
        G1["OU Model captures<br/>signals & trends effectively"]
        G2["Naive Model performs better<br/>on risk-return basis"]
        G3["Limitations: Non-stationary pairs,<br/>parameter tuning challenges"]
    end