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Optimal Multiple Trading Times Under the Exponential OU Model with Transaction Costs

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  • Tim Leung
  • Xin Li
  • Zheng Wang

Abstract

This paper studies the timing of trades under mean-reverting price dynamics subject to fixed transaction costs. We solve an optimal double stopping problem to determine the optimal times to enter and subsequently exit the market, when prices are driven by an exponential Ornstein-Uhlenbeck process. In addition, we analyze a related optimal switching problem that involves an infinite sequence of trades, and identify the conditions under which the double stopping and switching problems admit the same optimal entry and/or exit timing strategies. Among our results, we find that the investor generally enters when the price is low, but may find it optimal to wait if the current price is sufficiently close to zero. In other words, the continuation (waiting) region for entry is disconnected. Numerical results are provided to illustrate the dependence of timing strategies on model parameters and transaction costs.

Suggested Citation

  • Tim Leung & Xin Li & Zheng Wang, 2015. "Optimal Multiple Trading Times Under the Exponential OU Model with Transaction Costs," Papers 1504.04682, arXiv.org.
    • Handle: RePEc:arx:papers:1504.04682
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    References listed on IDEAS

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    2. Tim Leung & Peng Liu, 2012. "Risk Premia And Optimal Liquidation Of Credit Derivatives," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(08), pages 1-34.
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    7. Dayanik, Savas & Karatzas, Ioannis, 2003. "On the optimal stopping problem for one-dimensional diffusions," Stochastic Processes and their Applications, Elsevier, vol. 107(2), pages 173-212, October.
    8. Albert Shiryaev & Zuoquan Xu & Xun Yu Zhou, 2008. "Thou shalt buy and hold," Quantitative Finance, Taylor & Francis Journals, vol. 8(8), pages 765-776.
    9. 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.
    10. Tim Leung & Michael Ludkovski, 2010. "Optimal Timing to Purchase Options," Papers 1008.3650, arXiv.org, revised Apr 2011.
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    Citations

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    Cited by:

    1. Tim Leung & Jiao Li & Xin Li & Zheng Wang, 2016. "Speculative Futures Trading under Mean Reversion," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 23(4), pages 281-304, December.
    2. Zuo Quan Xu & Fahuai Yi, 2019. "Optimal redeeming strategy of stock loans under drift uncertainty," Papers 1901.06680, arXiv.org.
    3. Peng Huang & Tianxiang Wang, 2016. "On the Profitability of Optimal Mean Reversion Trading Strategies," Papers 1602.05858, arXiv.org.
    4. Tim Leung & Hongzhong Zhang, 2017. "Optimal Trading with a Trailing Stop," Papers 1701.03960, arXiv.org, revised Mar 2019.
    5. Jiao Li, 2016. "Trading VIX futures under mean reversion with regime switching," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 1-20, September.
    6. Alex S. L. Tse & Harry Zheng, 2023. "Speculative trading, prospect theory and transaction costs," Finance and Stochastics, Springer, vol. 27(1), pages 49-96, January.
    7. Guo, Kevin & Leung, Tim, 2017. "Understanding the non-convergence of agricultural futures via stochastic storage costs and timing options," Journal of Commodity Markets, Elsevier, vol. 6(C), pages 32-49.
    8. Yerkin Kitapbayev & Tim Leung, 2017. "Optimal mean-reverting spread trading: nonlinear integral equation approach," Annals of Finance, Springer, vol. 13(2), pages 181-203, May.
    9. Hongzhong Zhang, 2018. "Stochastic Drawdowns," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 10078, December.
    10. Jiao Li, 2016. "Trading VIX Futures under Mean Reversion with Regime Switching," Papers 1605.07945, arXiv.org, revised Jun 2016.
    11. Dahlgren, Eric & Leung, Tim, 2015. "An optimal multiple stopping approach to infrastructure investment decisions," Journal of Economic Dynamics and Control, Elsevier, vol. 53(C), pages 251-267.
    12. Tim Leung & Zheng Wang, 2019. "Optimal risk-averse timing of an asset sale: trending versus mean-reverting price dynamics," Annals of Finance, Springer, vol. 15(1), pages 1-28, March.
    13. Alex S. L. Tse & Harry Zheng, 2019. "Speculative Trading, Prospect Theory and Transaction Costs," Papers 1911.10106, arXiv.org, revised Oct 2022.
    14. Tim Leung & Xin Li & Zheng Wang, 2014. "Optimal Starting-Stopping and Switching of a CIR Process with Fixed Costs," Papers 1411.6080, arXiv.org.
    15. Yerkin Kitapbayev & Tim Leung, 2018. "Mean Reversion Trading With Sequential Deadlines And Transaction Costs," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(01), pages 1-22, February.
    16. Tim Leung & Zheng Wang, 2016. "Optimal Risk-Averse Timing of an Asset Sale: Trending vs Mean-Reverting Price Dynamics," Papers 1610.08143, arXiv.org.
    17. Phong Luu & Jingzhi Tie & Qing Zhang, 2018. "A Threshold Type Policy for Trading a Mean-Reverting Asset with Fixed Transaction Costs," Risks, MDPI, vol. 6(4), pages 1-15, September.
    18. Zuo Quan Xu & Fahuai Yi, 2020. "Optimal Redeeming Strategy of Stock Loans Under Drift Uncertainty," Mathematics of Operations Research, INFORMS, vol. 45(1), pages 384-401, February.

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