IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2311.15635.html
   My bibliography  Save this paper

Discretization of continuous-time arbitrage strategies in financial markets with fractional Brownian motion

Author

Listed:
  • Kerstin Lamert
  • Benjamin R. Auer
  • Ralf Wunderlich

Abstract

This study evaluates the practical usefulness of continuous-time arbitrage strategies designed to exploit serial correlation in fractional financial markets. Specifically, we revisit the strategies of \cite{Shiryaev1998} and \cite{Salopek1998} and transfer them to a real-world setting by distretizing their dynamics and introducing transaction costs. In Monte Carlo simulations with various market and trading parameter settings, we show that both are highly promising with respect to terminal portfolio values and loss probabilities. These features and complementary sparsity make them valuable additions to the toolkit of quantitative investors.

Suggested Citation

  • Kerstin Lamert & Benjamin R. Auer & Ralf Wunderlich, 2023. "Discretization of continuous-time arbitrage strategies in financial markets with fractional Brownian motion," Papers 2311.15635, arXiv.org.
    • Handle: RePEc:arx:papers:2311.15635
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2311.15635
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Badrinath, S.G. & Gubellini, S., 2011. "On the characteristics and performance of long-short, market-neutral and bear mutual funds," Journal of Banking & Finance, Elsevier, vol. 35(7), pages 1762-1776, July.
    2. K. J. Hong & S. Satchell, 2015. "Time series momentum trading strategy and autocorrelation amplification," Quantitative Finance, Taylor & Francis Journals, vol. 15(9), pages 1471-1487, September.
    3. Antonio Di Cesare & Philip A. Stork & Casper G. de Vries, 2015. "Risk Measures for Autocorrelated Hedge Fund Returns," Journal of Financial Econometrics, Oxford University Press, vol. 13(4), pages 868-895.
    4. Songzi Du & Haoxiang Zhu, 2017. "What is the Optimal Trading Frequency in Financial Markets?," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 84(4), pages 1606-1651.
    5. L. C. G. Rogers, 1997. "Arbitrage with Fractional Brownian Motion," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 95-105, January.
    6. Paolo Guasoni, 2006. "No Arbitrage Under Transaction Costs, With Fractional Brownian Motion And Beyond," Mathematical Finance, Wiley Blackwell, vol. 16(3), pages 569-582, July.
    7. Oleg Bondarenko, 2003. "Statistical Arbitrage and Securities Prices," The Review of Financial Studies, Society for Financial Studies, vol. 16(3), pages 875-919, July.
    8. Ben R. Marshall & Nhut H. Nguyen & Nuttawat Visaltanachoti, 2017. "Time series momentum and moving average trading rules," Quantitative Finance, Taylor & Francis Journals, vol. 17(3), pages 405-421, March.
    9. Rostek, S. & Schöbel, R., 2013. "A note on the use of fractional Brownian motion for financial modeling," Economic Modelling, Elsevier, vol. 30(C), pages 30-35.
    10. Pan, Ming-Shiun & Liano, Kartono & Huang, Gow-Cheng, 2004. "Industry momentum strategies and autocorrelations in stock returns," Journal of Empirical Finance, Elsevier, vol. 11(2), pages 185-202, March.
    11. Narasimhan Jegadeesh & Sheridan Titman, 2001. "Profitability of Momentum Strategies: An Evaluation of Alternative Explanations," Journal of Finance, American Finance Association, vol. 56(2), pages 699-720, April.
    12. Eling, Martin & Schuhmacher, Frank, 2007. "Does the choice of performance measure influence the evaluation of hedge funds?," Journal of Banking & Finance, Elsevier, vol. 31(9), pages 2632-2647, September.
    13. Jegadeesh, Narasimhan & Titman, Sheridan, 1993. "Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency," Journal of Finance, American Finance Association, vol. 48(1), pages 65-91, March.
    14. Brock, William & Lakonishok, Josef & LeBaron, Blake, 1992. "Simple Technical Trading Rules and the Stochastic Properties of Stock Returns," Journal of Finance, American Finance Association, vol. 47(5), pages 1731-1764, December.
    15. Harrison, J Michael & Pitbladdo, Richard & Schaefer, Stephen M, 1984. "Continuous Price Processes in Frictionless Markets Have Infinite Variation," The Journal of Business, University of Chicago Press, vol. 57(3), pages 353-365, July.
    16. Benjamin R Auer, 2016. "Pure return persistence, Hurst exponents and hedge fund selection – A practical note," Journal of Asset Management, Palgrave Macmillan, vol. 17(5), pages 319-330, September.
    17. Christopher Krauss, 2017. "Statistical Arbitrage Pairs Trading Strategies: Review And Outlook," Journal of Economic Surveys, Wiley Blackwell, vol. 31(2), pages 513-545, April.
    18. Jerry Coakley & Neil Kellard & Jian Wang, 2016. "Commodity futures returns: more memory than you might think!," The European Journal of Finance, Taylor & Francis Journals, vol. 22(14), pages 1457-1483, November.
    19. Cumova, Denisa & Nawrocki, David, 2014. "Portfolio optimization in an upside potential and downside risk framework," Journal of Economics and Business, Elsevier, vol. 71(C), pages 68-89.
    20. López-García, M.N. & Trinidad-Segovia, J.E. & Sánchez-Granero, M.A. & Pouchkarev, I., 2021. "Extending the Fama and French model with a long term memory factor," European Journal of Operational Research, Elsevier, vol. 291(2), pages 421-426.
    21. Hiemstra, Craig & Jones, Jonathan D., 1997. "Another look at long memory in common stock returns," Journal of Empirical Finance, Elsevier, vol. 4(4), pages 373-401, December.
    22. Malceniece, Laura & Malcenieks, Kārlis & Putniņš, Tālis J., 2019. "High frequency trading and comovement in financial markets," Journal of Financial Economics, Elsevier, vol. 134(2), pages 381-399.
    23. Chordia, Tarun & Subrahmanyam, Avanidhar & Tong, Qing, 2014. "Have capital market anomalies attenuated in the recent era of high liquidity and trading activity?," Journal of Accounting and Economics, Elsevier, vol. 58(1), pages 41-58.
    24. Rachev, Svetlozar & Jasic, Teo & Stoyanov, Stoyan & Fabozzi, Frank J., 2007. "Momentum strategies based on reward-risk stock selection criteria," Journal of Banking & Finance, Elsevier, vol. 31(8), pages 2325-2346, August.
    25. Erhan Bayraktar & H. Vincent Poor, 2005. "Arbitrage In Fractal Modulated Black–Scholes Models When The Volatility Is Stochastic," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(03), pages 283-300.
    26. Hogan, Steve & Jarrow, Robert & Teo, Melvyn & Warachka, Mitch, 2004. "Testing market efficiency using statistical arbitrage with applications to momentum and value strategies," Journal of Financial Economics, Elsevier, vol. 73(3), pages 525-565, September.
    27. Barroso, Pedro & Santa-Clara, Pedro, 2015. "Momentum has its moments," Journal of Financial Economics, Elsevier, vol. 116(1), pages 111-120.
    28. Schuhmacher, Frank & Eling, Martin, 2011. "Sufficient conditions for expected utility to imply drawdown-based performance rankings," Journal of Banking & Finance, Elsevier, vol. 35(9), pages 2311-2318, September.
    29. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    30. Paolo Guasoni & Yuliya Mishura & Miklós Rásonyi, 2021. "High-frequency trading with fractional Brownian motion," Finance and Stochastics, Springer, vol. 25(2), pages 277-310, April.
    31. Mikhail Simutin, 2014. "Cash Holdings and Mutual Fund Performance," Review of Finance, European Finance Association, vol. 18(4), pages 1425-1464.
    32. Juliana Nascimento & Warren Powell, 2010. "Dynamic Programming Models and Algorithms for the Mutual Fund Cash Balance Problem," Management Science, INFORMS, vol. 56(5), pages 801-815, May.
    33. Bessembinder, Hendrik, 2018. "Do stocks outperform Treasury bills?," Journal of Financial Economics, Elsevier, vol. 129(3), pages 440-457.
    Full references (including those not matched with items on IDEAS)

    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. Adam Zaremba & Jacob Koby Shemer, 2018. "Price-Based Investment Strategies," Springer Books, Springer, number 978-3-319-91530-2, December.
    2. Benjamin R. Auer, 2021. "Have trend-following signals in commodity futures markets become less reliable in recent years?," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 35(4), pages 533-553, December.
    3. Chaonan Lin & Nien‐Tzu Yang & Robin K. Chou & Kuan‐Cheng Ko, 2022. "A timing momentum strategy," Accounting and Finance, Accounting and Finance Association of Australia and New Zealand, vol. 62(S1), pages 1339-1379, April.
    4. Stadtmüller, Immo & Auer, Benjamin R. & Schuhmacher, Frank, 2022. "On the time-varying dynamics of stock and commodity momentum returns," Finance Research Letters, Elsevier, vol. 46(PB).
    5. Zhu, Zhaobo & Duan, Xinrui & Sun, Licheng & Tu, Jun, 2019. "Momentum and reversal: The role of short selling," Journal of Economic Dynamics and Control, Elsevier, vol. 104(C), pages 95-110.
    6. Shynkevich, Andrei, 2013. "Time-series momentum as an intra- and inter-industry effect: Implications for market efficiency," Journal of Economics and Business, Elsevier, vol. 69(C), pages 64-85.
    7. Ming‐Yu Liu, 2019. "Improving momentum strategies using residual returns and option‐implied information," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(4), pages 499-521, April.
    8. Valeriy Zakamulin & Javier Giner, 2020. "Trend following with momentum versus moving averages: a tale of differences," Quantitative Finance, Taylor & Francis Journals, vol. 20(6), pages 985-1007, June.
    9. Li, Zeming & Sakkas, Athanasios & Urquhart, Andrew, 2022. "Intraday time series momentum: Global evidence and links to market characteristics," Journal of Financial Markets, Elsevier, vol. 57(C).
    10. Subrahmanyam, Avanidhar, 2018. "Equity market momentum: A synthesis of the literature and suggestions for future work," Pacific-Basin Finance Journal, Elsevier, vol. 51(C), pages 291-296.
    11. Fernando F. Ferreira & A. Christian Silva & Ju-Yi Yen, 2014. "Information ratio analysis of momentum strategies," Papers 1402.3030, arXiv.org, revised Jul 2014.
    12. Pätäri, Eero & Ahmed, Sheraz & Luukka, Pasi & Yeomans, Julian Scott, 2023. "Can monthly-return rank order reveal a hidden dimension of momentum? The post-cost evidence from the U.S. stock markets," The North American Journal of Economics and Finance, Elsevier, vol. 65(C).
    13. Hong, KiHoon & Wu, Eliza, 2016. "The roles of past returns and firm fundamentals in driving US stock price movements," International Review of Financial Analysis, Elsevier, vol. 43(C), pages 62-75.
    14. Jarrow, Robert & Teo, Melvyn & Tse, Yiu Kuen & Warachka, Mitch, 2012. "An improved test for statistical arbitrage," Journal of Financial Markets, Elsevier, vol. 15(1), pages 47-80.
    15. Marianna Brunetti & Roberta De Luca, 2020. "Pre-selection in Cointegration-based Pairs Trading," CEIS Research Paper 500, Tor Vergata University, CEIS, revised 10 Mar 2021.
    16. Kim, Byungoh & Suh, Sangwon, 2018. "Sentiment-based momentum strategy," International Review of Financial Analysis, Elsevier, vol. 58(C), pages 52-68.
    17. Farias Nazário, Rodolfo Toríbio & e Silva, Jéssica Lima & Sobreiro, Vinicius Amorim & Kimura, Herbert, 2017. "A literature review of technical analysis on stock markets," The Quarterly Review of Economics and Finance, Elsevier, vol. 66(C), pages 115-126.
    18. Fangming Xu & Huainan Zhao & Liyi Zheng, 2022. "Investment momentum: A two‐dimensional behavioural strategy," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 27(1), pages 1191-1207, January.
    19. Fernando F. Ferreira & A. Christian Silva & Ju-Yi Yen, 2019. "Detailed study of a moving average trading rule," Papers 1907.00212, arXiv.org.
    20. Stephen A. Gorman & Frank J. Fabozzi, 2021. "The ABC’s of the alternative risk premium: academic roots," Journal of Asset Management, Palgrave Macmillan, vol. 22(6), pages 405-436, October.

    More about this item

    Statistics

    Access and download statistics

    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:arx:papers:2311.15635. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.