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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 Shiryaev (1998) and Salopek (1998) 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 as well as a formal analysis of discretization error, we show that both are promising with respect to terminal portfolio values and loss probabilities. These features and complementary sparsity make them worth serious consideration in 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, revised Dec 2024.
    • Handle: RePEc:arx:papers:2311.15635
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Barroso, Pedro & Santa-Clara, Pedro, 2015. "Momentum has its moments," Journal of Financial Economics, Elsevier, vol. 116(1), pages 111-120.
    10. 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.
    11. 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.
    12. 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.
    13. Oleg Bondarenko, 2003. "Statistical Arbitrage and Securities Prices," The Review of Financial Studies, Society for Financial Studies, vol. 16(3), pages 875-919, July.
    14. 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.
    15. 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.
    16. Salopek, D. M., 1998. "Tolerance to arbitrage," Stochastic Processes and their Applications, Elsevier, vol. 76(2), pages 217-230, August.
    17. 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.
    18. Christopher Krauss, 2017. "Statistical Arbitrage Pairs Trading Strategies: Review And Outlook," Journal of Economic Surveys, Wiley Blackwell, vol. 31(2), pages 513-545, April.
    19. 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.
    20. 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.
    21. Mikhail Simutin, 2014. "Cash Holdings and Mutual Fund Performance," Review of Finance, European Finance Association, vol. 18(4), pages 1425-1464.
    22. Frazzini, Andrea & Pedersen, Lasse Heje, 2014. "Betting against beta," Journal of Financial Economics, Elsevier, vol. 111(1), pages 1-25.
    23. 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.
    24. 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.
    25. 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.
    26. 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.
    27. 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.
    28. Bessembinder, Hendrik, 2018. "Do stocks outperform Treasury bills?," Journal of Financial Economics, Elsevier, vol. 129(3), pages 440-457.
    29. 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.
    30. 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.
    31. 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.
    32. 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.
    33. 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.
    34. 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.
    35. L. C. G. Rogers, 1997. "Arbitrage with Fractional Brownian Motion," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 95-105, January.
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