Paper: arXiv 2403.12180

Abstract

Statistical arbitrage is a prevalent trading strategy which takes advantage of mean reverse property of spread of paired stocks. Studies on this strategy often rely heavily on model assumption. In this study, we introduce an innovative model-free and reinforcement learning based framework for statistical arbitrage. For the construction of mean reversion spreads, we establish an empirical reversion time metric and optimize asset coefficients by minimizing this empirical mean reversion time. In the trading phase, we employ a reinforcement learning framework to identify the optimal mean reversion strategy. Diverging from traditional mean reversion strategies that primarily focus on price deviations from a long-term mean, our methodology creatively constructs the state space to encapsulate the recent trends in price movements. Additionally, the reward function is carefully tailored to reflect the unique characteristics of mean reversion trading.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 4.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper employs advanced stochastic calculus (Ornstein-Uhlenbeck processes) and reinforcement learning algorithms, indicating high mathematical density. While it tests on real-world US stock data, the reliance on simulated data for algorithm validation and the focus on theoretical framework over detailed implementation specifics (like transaction costs) places it more in the research lab than ready for the trading desk.

Research Flowchart

  flowchart TD
  A["Research Goal: Model-Free<br>Statistical Arbitrage"] --> B["Inputs: Historical<br>Stock Price Data"]
  B --> C["Spread Construction:<br>Minimize Empirical Mean Reversion Time"]
  C --> D["Trading Framework:<br>Reinforcement Learning RL"]
  D --> E["State Space:<br>Recent Price Trends"]
  D --> F["Reward Function:<br>Tailored for Mean Reversion"]
  E & F --> G["Key Findings:<br>Optimal Trading Strategy &<br>Model-Free ARBITRAGE"]

Cited References (34)

  1. Pairs trading: Performance of a relative-value arbitrage rule (2006)
  2. Statistical arbitrage in the US equities market (2010)
  3. Dynamic Modeling of Mean Reverting Spreads for Statistical Arbitrage (2011)
  4. Optimal Mean Reversion Trading: Mathematical Analysis and Practical Applications (2016)
  5. Optimal mean reversion trading with transaction costs and stop-loss exit (2015)
  6. Arbitrage in Stock Index Futures (1990)
  7. Optimal arbitrage strategies on stock index futures under position limits (2011)
  8. A profit model for spread trading with an application to energy futures (2010)
and 26 more
  1. Dynamic modeling of mean-reverting spreads for statistical arbitrage (2011)
  2. Identifying small mean-reverting portfolios (2011)
  3. Sparse Mean-Reverting Portfolios via Penalized Likelihood Optimization (2020)
  4. Constructing cointegrated cryptocurrency portfolios for statistical arbitrage (2019)
  5. Are pairs trading profits robust to trading costs? (2012)
  6. Pairs Trading: quantitative methods and analysis (2004)
  7. Co-integration and error correction: representation, estimation, and testing (1987)
  8. Trading in the presence of cointegration (2012)
  9. Pairs trading and selection methods: is cointegration superior? (2015)
  10. Pairs trading (2005)
  11. A new approach to modeling and estimation for pairs trading (2006)
  12. On the efficacy of optimized exit rule for mean reversion trading (2020)
  13. Sparse mean-reverting portfolios via penalized likelihood optimization (2020)
  14. Pairs trading: A copula approach (2013)
  15. Pairs trading with copulas (2016)
  16. Deep Learning Statistical Arbitrage (2021)
  17. Enhancing a pairs trading strategy with the application of machine learning (2020)
  18. Pairs trading on different portfolios based on machine learning (2021)
  19. Optimal liquidation of a pairs trade (2011)
  20. Stochastic optimization methods for buying-low-and-selling-high strategies (2009)
  21. Differential equations driven by rough paths (2007)
  22. A primer on the signature method in machine learning (2016) — link
  23. Optimal execution with rough path signatures (2020)
  24. Optimal stopping with signatures (2021) — link
  25. Uniqueness for the signature of a path of bounded variation and the reduced path group (2010)
  26. Important extrema of time series (2007)

0 of 34 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.