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A Stochastic Approximation Approach for Trend-Following Trading

In: Hidden Markov Models in Finance

Author

Listed:
  • Duy Nguyen

    (The University of Georgia)

  • George Yin

    (Wayne State University)

  • Qing Zhang

    (The University of Georgia)

Abstract

This work develops a feasible computation procedure for trend-following trading under a bull-bear switching market model. In the asset model, the drift of the stock price switches between two parameters corresponding to an uptrend (bull market) and a downtrend (bear market) according to a partially observable Markov chain. The objective is to buy and sell the underlying stock to maximize an expected return. It is shown in Dai et al. (SIAM J Financ Math 1:780–810, 2010; Optimal trend following trading rules. Working paper) that an optimal trading strategy can be obtained in terms of two threshold levels. Finding the threshold levels turns out to be a difficult task. In this paper, we develop a stochastic approximation algorithm to approximate the threshold levels. One of the main advantages of this approach is that one need not solve the associated HJB equations. We also establish the convergence of the algorithm and provide numerical examples to illustrate the results.

Suggested Citation

  • Duy Nguyen & George Yin & Qing Zhang, 2014. "A Stochastic Approximation Approach for Trend-Following Trading," International Series in Operations Research & Management Science, in: Rogemar S. Mamon & Robert J. Elliott (ed.), Hidden Markov Models in Finance, edition 127, chapter 0, pages 167-184, Springer.
    • Handle: RePEc:spr:isochp:978-1-4899-7442-6_7
    DOI: 10.1007/978-1-4899-7442-6_7
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    Citations

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    Cited by:

    1. J. X. Jiang & R. H. Liu & D. Nguyen, 2016. "A Recombining Tree Method For Option Pricing With State-Dependent Switching Rates," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(02), pages 1-26, March.
    2. Zakamulin, Valeriy & Giner, Javier, 2023. "Optimal trend-following with transaction costs," International Review of Financial Analysis, Elsevier, vol. 90(C).

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