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Optimal trading strategies for Itô diffusion processes

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  • Bertram, William K.

Abstract

In this paper we present a method for determining optimal trading strategies for Itô diffusion processes. By framing the problem in terms of the first passage time for the process we derive distribution and density functions for the trade length and use these functions to calculate the expected trading frequency for the strategy. The expected value and the variance of the rate of profit are obtained as functions of the return per trade and trading frequency. We present two measures for trade drawdown which may be used as constraints when determining an optimal strategy. The optimal strategy is calculated for the Ornstein–Uhlenbeck process by maximising the expected rate of profit.

Suggested Citation

  • Bertram, William K., 2009. "Optimal trading strategies for Itô diffusion processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(14), pages 2865-2873.
    • Handle: RePEc:eee:phsmap:v:388:y:2009:i:14:p:2865-2873
    DOI: 10.1016/j.physa.2009.04.004
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    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. Baviera, Roberto & Santagostino Baldi, Tommaso, 2019. "Stop-loss and leverage in optimal statistical arbitrage with an application to energy market," Energy Economics, Elsevier, vol. 79(C), pages 130-143.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.

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