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The Optimal Limit Prices of Limit Orders under an Extended Geometric Brownian Motion with Bankruptcy Risk

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  • Yu-Sheng Hsu

    (Department of Mathematics, National Central University, Chung-Li 320317, Taiwan)

  • Pei-Chun Chen

    (Department of Data Science and Big Data Analytics, Providence University, Taichung City 433303, Taiwan)

  • Cheng-Hsun Wu

    (Department of Financial Engineering and Actuarial Mathematics, Soochow University, Taipei City 100006, Taiwan)

Abstract

In the Black and Scholes system, the underlying asset price model follows geometric Brownian motion (GBM) with no bankruptcy risk. While GBM is a commonly used model in financial markets, bankruptcy risk should be considered in the case of a severe economic crisis, such as that caused by the COVID-19 pandemic. The omission of bankruptcy risk could considerably influence the setting of a trading strategy. In this article, we adopt an extended GBM model that considers the bankruptcy risk and study its optimal limit price problem. A limit order is a classical trading strategy for investing in stocks. First, we construct the explicit expressions of the expected discounted profit functions for sell and buy limit orders and then derive their optimal limit prices. Furthermore, via sensitivity analysis, we discuss the influence of the omission of bankruptcy risk in executing limit orders.

Suggested Citation

  • Yu-Sheng Hsu & Pei-Chun Chen & Cheng-Hsun Wu, 2020. "The Optimal Limit Prices of Limit Orders under an Extended Geometric Brownian Motion with Bankruptcy Risk," Mathematics, MDPI, vol. 9(1), pages 1-13, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2020:i:1:p:54-:d:469927
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    References listed on IDEAS

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    5. Goodell, John W., 2020. "COVID-19 and finance: Agendas for future research," Finance Research Letters, Elsevier, vol. 35(C).
    6. Robert McDonald & Daniel Siegel, 1986. "The Value of Waiting to Invest," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 101(4), pages 707-727.
    7. Rostek, S. & Schöbel, R., 2013. "A note on the use of fractional Brownian motion for financial modeling," Economic Modelling, Elsevier, vol. 30(C), pages 30-35.
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