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On a Data-Driven Optimization Approach to the PID-Based Algorithmic Trading

Author

Listed:
  • Vadim Azhmyakov

    (Data Analytics, Universidad Central, Bogota 11001, Colombia
    These authors contributed equally to this work.)

  • Ilya Shirokov

    (Algorithmic Systems Corp, Phuket 83000, Thailand
    These authors contributed equally to this work.)

  • Yuri Dernov

    (Algorithmic Systems Corp, Phuket 83000, Thailand
    These authors contributed equally to this work.)

  • Luz Adriana Guzman Trujillo

    (LARIS, Université d’Angers, 49000 Angers, France
    These authors contributed equally to this work.)

Abstract

This paper proposes an optimal trading algorithm based on a novel application of conventional control engineering (CE). We consider a fundamental CE concept, namely, the feedback control, and apply it to algorithmic trading (AT). The concrete feedback control strategy is designed in a form of the celebrated proportional–integral–derivative (PID) model. The highly fluctuating nature of the modern financial markets has led to the adoption of a model-free realization of the generic PID framework. The control theoretical methodology we propose is combined with the advanced statistics for the historical market data. We obtain a specific log-normal probability distribution function (pdf) associated with the specific quantities associated with the available stock data. The empirical log-normal pdf mentioned above enables the necessary PID gains optimization. For this aim, we apply the data-driven optimization approaches and consider the corresponding Monte Carlo solution procedure. The optimized PID trading algorithm we propose is also studied in the Fourier analysis framework. This equivalent frequency domain representation involves a new concept in financial engineering, namely, the “stock market energy” concept. For the evaluation, we implement the proposed PID optimal trading algorithm and develop a Python-based prototype software. We finally apply the corresponding prototype software to a data set from the Binance BTC/USDT (Bitcoin/Tether) stock market. The experimental result illustrates the implementability of the proposed optimal PID trading scheme and also shows the effectiveness of the proposed CE methods in the modern AT.

Suggested Citation

  • Vadim Azhmyakov & Ilya Shirokov & Yuri Dernov & Luz Adriana Guzman Trujillo, 2023. "On a Data-Driven Optimization Approach to the PID-Based Algorithmic Trading," JRFM, MDPI, vol. 16(9), pages 1-18, August.
    • Handle: RePEc:gam:jjrfmx:v:16:y:2023:i:9:p:387-:d:1228915
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    References listed on IDEAS

    as
    1. Antoniou, I & Ivanov, Vi.V & Ivanov, Va.V & Zrelov, P.V, 2004. "On the log-normal distribution of stock market data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 331(3), pages 617-638.
    2. 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.
    3. Bertsimas, Dimitris & Lo, Andrew W., 1998. "Optimal control of execution costs," Journal of Financial Markets, Elsevier, vol. 1(1), pages 1-50, April.
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