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Stop-loss and Leverage in optimal Statistical Arbitrage with an application to Energy market

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  • Roberto Baviera
  • Tommaso Santagostino Baldi

Abstract

In this paper we develop a statistical arbitrage trading strategy with two key elements in hi-frequency trading: stop-loss and leverage. We consider, as in Bertram (2009), a mean-reverting process for the security price with proportional transaction costs; we show how to introduce stop-loss and leverage in an optimal trading strategy. We focus on repeated strategies using a self-financing portfolio. For every given stop-loss level we derive analytically the optimal investment strategy consisting of optimal leverage and market entry/exit levels. First we show that the optimal strategy a' la Bertram depends on the probabilities to reach entry/exit levels, on expected First-Passage-Times and on expected First-Exit-Times from an interval. Then, when the underlying log-price follows an Ornstein-Uhlenbeck process, we deduce analytical expressions for expected First-Exit-Times and we derive the long-run return of the strategy as an elementary function of the stop-loss. Following industry practice of pairs trading we consider an example of pair in the energy futures' market, reporting in detail the analysis for a spread on Heating-Oil and Gas-Oil futures in one year sample of half-an-hour market prices.

Suggested Citation

  • Roberto Baviera & Tommaso Santagostino Baldi, 2017. "Stop-loss and Leverage in optimal Statistical Arbitrage with an application to Energy market," Papers 1706.07021, arXiv.org.
  • Handle: RePEc:arx:papers:1706.07021
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    File URL: http://arxiv.org/pdf/1706.07021
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    References listed on IDEAS

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    1. Robert Elliott & John Van Der Hoek & William Malcolm, 2005. "Pairs trading," Quantitative Finance, Taylor & Francis Journals, vol. 5(3), pages 271-276.
    2. Jun Yu & Peter C. B. Phillips, 2001. "A Gaussian approach for continuous time models of the short-term interest rate," Econometrics Journal, Royal Economic Society, vol. 4(2), pages 1-3.
    3. Evan Gatev & William N. Goetzmann & K. Geert Rouwenhorst, 2006. "Pairs Trading: Performance of a Relative-Value Arbitrage Rule," Review of Financial Studies, Society for Financial Studies, vol. 19(3), pages 797-827.
    4. Mark Cummins & Andrea Bucca, 2012. "Quantitative spread trading on crude oil and refined products markets," Quantitative Finance, Taylor & Francis Journals, vol. 12(12), pages 1857-1875, December.
    5. Michael Taksar & Michael J. Klass & David Assaf, 1988. "A Diffusion Model for Optimal Portfolio Selection in the Presence of Brokerage Fees," Mathematics of Operations Research, INFORMS, vol. 13(2), pages 277-294, May.
    6. repec:wsi:ijtafx:v:18:y:2015:i:03:n:s021902491550020x is not listed on IDEAS
    7. 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.
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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.

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