IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v389y2010i11p2234-2243.html
   My bibliography  Save this article

Analytic solutions for optimal statistical arbitrage trading

Author

Listed:
  • Bertram, William K.

Abstract

In this paper we derive analytic formulae for statistical arbitrage trading where the security price follows an Ornstein–Uhlenbeck process. By framing the problem in terms of the first-passage time of the process, we derive expressions for the mean and variance of the trade length and the return. We examine the problem of choosing an optimal strategy under two different objective functions: the expected return, and the Sharpe ratio. An exact analytic solution is obtained for the case of maximising the expected return.

Suggested Citation

  • Bertram, William K., 2010. "Analytic solutions for optimal statistical arbitrage trading," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(11), pages 2234-2243.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:11:p:2234-2243
    DOI: 10.1016/j.physa.2010.01.045
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437110001019
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2010.01.045?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Gençay, Ramazan & Dacorogna, Michel & Muller, Ulrich A. & Pictet, Olivier & Olsen, Richard, 2001. "An Introduction to High-Frequency Finance," Elsevier Monographs, Elsevier, edition 1, number 9780122796715.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Endres, Sylvia & Stübinger, Johannes, 2017. "Optimal trading strategies for Lévy-driven Ornstein-Uhlenbeck processes," FAU Discussion Papers in Economics 17/2017, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.
    2. Matthew Clegg & Christopher Krauss, 2018. "Pairs trading with partial cointegration," Quantitative Finance, Taylor & Francis Journals, vol. 18(1), pages 121-138, January.
    3. Ahmet Göncü & Erdinc Akyildirim, 2016. "A stochastic model for commodity pairs trading," Quantitative Finance, Taylor & Francis Journals, vol. 16(12), pages 1843-1857, December.
    4. Stübinger, Johannes & Endres, Sylvia, 2017. "Pairs trading with a mean-reverting jump-diffusion model on high-frequency data," FAU Discussion Papers in Economics 10/2017, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.
    5. Yaoyuan Zhang & Dewen Xiong, 2023. "Optimal Strategy of the Dynamic Mean-Variance Problem for Pairs Trading under a Fast Mean-Reverting Stochastic Volatility Model," Mathematics, MDPI, vol. 11(9), pages 1-19, May.
    6. Viviana Fanelli & Claudio Fontana & Francesco Rotondi, 2023. "A hidden Markov model for statistical arbitrage in international crude oil futures markets," Papers 2309.00875, arXiv.org, revised Sep 2024.
    7. Alexander Lipton & Marcos Lopez de Prado, 2020. "A closed-form solution for optimal mean-reverting trading strategies," Papers 2003.10502, arXiv.org.
    8. Erdinc Akyildirim & Ahmet Goncu & Alper Hekimoglu & Duc Khuong Nguyen & Ahmet Sensoy, 2023. "Statistical arbitrage: factor investing approach," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 45(4), pages 1295-1331, December.
    9. Tim Leung & Xin Li, 2015. "Optimal Mean Reversion Trading With Transaction Costs And Stop-Loss Exit," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(03), pages 1-31.
    10. Haican Diao & Guoshan Liu & Zhuangming Zhu, 2020. "Research on a stock-matching trading strategy based on bi-objective optimization," Frontiers of Business Research in China, Springer, vol. 14(1), pages 1-14, December.
    11. Kasper Johansson & Thomas Schmelzer & Stephen Boyd, 2024. "Finding Moving-Band Statistical Arbitrages via Convex-Concave Optimization," Papers 2402.08108, arXiv.org.
    12. Marianna Brunetti & Roberta De Luca, 2022. "Sensitivity of Profitability in Cointegration-Based Pairs Trading," CEIS Research Paper 540, Tor Vergata University, CEIS, revised 11 Apr 2022.
    13. Johannes Stübinger & Lucas Schneider, 2019. "Statistical Arbitrage with Mean-Reverting Overnight Price Gaps on High-Frequency Data of the S&P 500," JRFM, MDPI, vol. 12(2), pages 1-19, April.
    14. Kiyoshi Suzuki, 2018. "Optimal pair-trading strategy over long/short/square positions—empirical study," Quantitative Finance, Taylor & Francis Journals, vol. 18(1), pages 97-119, January.
    15. Krauss, Christopher, 2015. "Statistical arbitrage pairs trading strategies: Review and outlook," FAU Discussion Papers in Economics 09/2015, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.
    16. Vladimír Holý & Michal Černý, 2022. "Bertram’s pairs trading strategy with bounded risk," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 30(2), pages 667-682, June.
    17. Jeff Stephenson & Bruce Vanstone & Tobias Hahn, 2021. "A Unifying Model for Statistical Arbitrage: Model Assumptions and Empirical Failure," Computational Economics, Springer;Society for Computational Economics, vol. 58(4), pages 943-964, December.
    18. Wang, Xi & Bao, Si & Chen, Jingchao, 2017. "High-frequency stock linkage and multi-dimensional stationary processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 70-83.
    19. Endres, Sylvia & Stübinger, Johannes, 2018. "A flexible regime switching model with pairs trading application to the S&P 500 high-frequency stock returns," FAU Discussion Papers in Economics 07/2018, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.
    20. Johannes Stübinger & Sylvia Endres, 2018. "Pairs trading with a mean-reverting jump–diffusion model on high-frequency data," Quantitative Finance, Taylor & Francis Journals, vol. 18(10), pages 1735-1751, October.
    21. Kim, Min Jae & Kim, Sehyun & Jo, Yong Hwan & Kim, Soo Yong, 2011. "Dependence structure of the commodity and stock markets, and relevant multi-spread strategy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(21), pages 3842-3854.
    22. Zhengqin Zeng & Chi-Guhn Lee, 2014. "Pairs trading: optimal thresholds and profitability," Quantitative Finance, Taylor & Francis Journals, vol. 14(11), pages 1881-1893, November.
    23. Roy Cerqueti & Viviana Fanelli, 2021. "Long memory and crude oil’s price predictability," Annals of Operations Research, Springer, vol. 299(1), pages 895-906, April.
    24. Vladim'ir Hol'y & Petra Tomanov'a, 2018. "Estimation of Ornstein-Uhlenbeck Process Using Ultra-High-Frequency Data with Application to Intraday Pairs Trading Strategy," Papers 1811.09312, arXiv.org, revised Jul 2022.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dash, Saumya Ranjan & Maitra, Debasish, 2018. "Does sentiment matter for stock returns? Evidence from Indian stock market using wavelet approach," Finance Research Letters, Elsevier, vol. 26(C), pages 32-39.
    2. Lallouache, Mehdi & Abergel, Frédéric, 2014. "Tick size reduction and price clustering in a FX order book," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 488-498.
    3. Dufour, Jean-Marie & García, René, 2008. "Measuring causality between volatility and returns with high-frequency data," UC3M Working papers. Economics we084422, Universidad Carlos III de Madrid. Departamento de Economía.
    4. Kaijian He & Rui Zha & Jun Wu & Kin Keung Lai, 2016. "Multivariate EMD-Based Modeling and Forecasting of Crude Oil Price," Sustainability, MDPI, vol. 8(4), pages 1-11, April.
    5. Ozcan Ceylan, 2015. "Limited information-processing capacity and asymmetric stock correlations," Quantitative Finance, Taylor & Francis Journals, vol. 15(6), pages 1031-1039, June.
    6. Scalas, Enrico & Kaizoji, Taisei & Kirchler, Michael & Huber, Jürgen & Tedeschi, Alessandra, 2006. "Waiting times between orders and trades in double-auction markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 366(C), pages 463-471.
    7. Nour Meddahi, 2002. "A theoretical comparison between integrated and realized volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 479-508.
    8. Ole E. Barndorff-Nielsen & Neil Shephard, 2006. "Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation," Journal of Financial Econometrics, Oxford University Press, vol. 4(1), pages 1-30.
    9. Monira Essa Aloud, 2016. "Time Series Analysis Indicators under Directional Changes: The Case of Saudi Stock Market," International Journal of Economics and Financial Issues, Econjournals, vol. 6(1), pages 55-64.
    10. Vassilios G. Papavassiliou, 2016. "Allowing For Jump Measurements In Volatility: A High-Frequency Financial Data Analysis Of Individual Stocks," Bulletin of Economic Research, Wiley Blackwell, vol. 68(2), pages 124-132, April.
    11. Monira Essa Aloud, 2016. "Profitability of Directional Change Based Trading Strategies: The Case of Saudi Stock Market," International Journal of Economics and Financial Issues, Econjournals, vol. 6(1), pages 87-95.
    12. Cotter, John & Dowd, Kevin, 2007. "The tail risks of FX return distributions: A comparison of the returns associated with limit orders and market orders," Finance Research Letters, Elsevier, vol. 4(3), pages 146-154, September.
    13. Selçuk, Faruk & Gençay, Ramazan, 2006. "Intraday dynamics of stock market returns and volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 375-387.
    14. Stefanescu, Razvan & Dumitriu, Ramona, 2015. "Conţinutul analizei seriilor de timp financiare [The Essentials of the Analysis of Financial Time Series]," MPRA Paper 67175, University Library of Munich, Germany.
    15. Challet, Damien & Stinchcombe, Robin, 2003. "Limit order market analysis and modelling: on a universal cause for over-diffusive prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 141-145.
    16. Feng, Yuanhua, 2002. "Modelling Different Volatility Components," CoFE Discussion Papers 02/18, University of Konstanz, Center of Finance and Econometrics (CoFE).
    17. Caporin, Massimiliano & Chang, Chia-Lin & McAleer, Michael, 2019. "Are the S&P 500 index and crude oil, natural gas and ethanol futures related for intra-day data?," International Review of Economics & Finance, Elsevier, vol. 59(C), pages 50-70.
    18. Gencay, Ramazan & Selcuk, Faruk & Ulugulyagci, Abdurrahman, 2003. "High volatility, thick tails and extreme value theory in value-at-risk estimation," Insurance: Mathematics and Economics, Elsevier, vol. 33(2), pages 337-356, October.
    19. Julien Chevallier & Benoît Sévi, 2011. "On the realized volatility of the ECX CO 2 emissions 2008 futures contract: distribution, dynamics and forecasting," Annals of Finance, Springer, vol. 7(1), pages 1-29, February.
    20. Masanori Hirano & Kiyoshi Izumi & Hiroyasu Matsushima & Hiroki Sakaji, 2020. "Comparing Actual and Simulated HFT Traders' Behavior for Agent Design," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 23(3), pages 1-6.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:389:y:2010:i:11:p:2234-2243. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.