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Optimal execution with rough path signatures

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  • Jasdeep Kalsi
  • Terry Lyons
  • Imanol Perez Arribas

Abstract

We present a method for obtaining approximate solutions to the problem of optimal execution, based on a signature method. The framework is general, only requiring that the price process is a geometric rough path and the price impact function is a continuous function of the trading speed. Following an approximation of the optimisation problem, we are able to calculate an optimal solution for the trading speed in the space of linear functions on a truncation of the signature of the price process. We provide strong numerical evidence illustrating the accuracy and flexibility of the approach. Our numerical investigation both examines cases where exact solutions are known, demonstrating that the method accurately approximates these solutions, and models where exact solutions are not known. In the latter case, we obtain favourable comparisons with standard execution strategies.

Suggested Citation

  • Jasdeep Kalsi & Terry Lyons & Imanol Perez Arribas, 2019. "Optimal execution with rough path signatures," Papers 1905.00728, arXiv.org.
    • Handle: RePEc:arx:papers:1905.00728
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    File URL: http://arxiv.org/pdf/1905.00728
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    References listed on IDEAS

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    1. �lvaro Cartea & Sebastian Jaimungal, 2015. "Optimal execution with limit and market orders," Quantitative Finance, Taylor & Francis Journals, vol. 15(8), pages 1279-1291, August.
    2. Iacopo Mastromatteo & Michael Benzaquen & Zoltan Eisler & Jean-Philippe Bouchaud, 2017. "Trading Lightly: Cross-Impact and Optimal Portfolio Execution," Papers 1702.03838, arXiv.org, revised Aug 2017.
    3. Paolo Pasquariello & Clara Vega, 2015. "Strategic Cross-Trading in the U.S. Stock Market," Review of Finance, European Finance Association, vol. 19(1), pages 229-282.
    4. Gianbiagio Curato & Jim Gatheral & Fabrizio Lillo, 2017. "Optimal execution with non-linear transient market impact," Quantitative Finance, Taylor & Francis Journals, vol. 17(1), pages 41-54, January.
    5. Charles-Albert Lehalle & Eyal Neuman, 2019. "Incorporating signals into optimal trading," Finance and Stochastics, Springer, vol. 23(2), pages 275-311, April.
    6. Bertsimas, Dimitris & Lo, Andrew W., 1998. "Optimal control of execution costs," Journal of Financial Markets, Elsevier, vol. 1(1), pages 1-50, April.
    7. Bence Toth & Yves Lemperiere & Cyril Deremble & Joachim de Lataillade & Julien Kockelkoren & Jean-Philippe Bouchaud, 2011. "Anomalous price impact and the critical nature of liquidity in financial markets," Papers 1105.1694, arXiv.org, revised Nov 2011.
    8. Candia Riga, 2016. "A pathwise approach to continuous-time trading," Papers 1602.04946, arXiv.org.
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    Cited by:

    1. Christa Cuchiero & Janka Moller, 2023. "Signature Methods in Stochastic Portfolio Theory," Papers 2310.02322, arXiv.org, revised Mar 2024.

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