IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2020i1p54-d469927.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/1/54/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/1/54/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Zhang, Dayong & Hu, Min & Ji, Qiang, 2020. "Financial markets under the global pandemic of COVID-19," Finance Research Letters, Elsevier, vol. 36(C).
    2. 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.
    3. 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.
    4. Albert Shiryaev & Zuoquan Xu & Xun Yu Zhou, 2008. "Thou shalt buy and hold," Quantitative Finance, Taylor & Francis Journals, vol. 8(8), pages 765-776.
    5. Lo, Andrew W. & MacKinlay, A. Craig & Zhang, June, 2002. "Econometric models of limit-order executions," Journal of Financial Economics, Elsevier, vol. 65(1), pages 31-71, July.
    6. Handa, Puneet & Schwartz, Robert A, 1996. "Limit Order Trading," Journal of Finance, American Finance Association, vol. 51(5), pages 1835-1861, December.
    7. Goodell, John W., 2020. "COVID-19 and finance: Agendas for future research," Finance Research Letters, Elsevier, vol. 35(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Heyden, Kim J. & Heyden, Thomas, 2021. "Market reactions to the arrival and containment of COVID-19: An event study," Finance Research Letters, Elsevier, vol. 38(C).
    2. Mahata, Ajit & Rai, Anish & Nurujjaman, Md. & Prakash, Om, 2021. "Modeling and analysis of the effect of COVID-19 on the stock price: V and L-shape recovery," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 574(C).
    3. Al-Maadid, Alanoud & Alhazbi, Saleh & Al-Thelaya, Khaled, 2022. "Using machine learning to analyze the impact of coronavirus pandemic news on the stock markets in GCC countries," Research in International Business and Finance, Elsevier, vol. 61(C).
    4. Wei‐Yu Kuo & Ching‐Ting Lin, 2018. "Trader types and fleeting orders: Evidence from Taiwan Futures Exchange," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 38(12), pages 1443-1469, December.
    5. Yousfi, Mohamed & Ben Zaied, Younes & Ben Cheikh, Nidhaleddine & Ben Lahouel, Béchir & Bouzgarrou, Houssem, 2021. "Effects of the COVID-19 pandemic on the US stock market and uncertainty: A comparative assessment between the first and second waves," Technological Forecasting and Social Change, Elsevier, vol. 167(C).
    6. Amin Jan & Mário Nuno Mata & Pia A. Albinsson & José Moleiro Martins & Rusni Bt Hassan & Pedro Neves Mata, 2021. "Alignment of Islamic Banking Sustainability Indicators with Sustainable Development Goals: Policy Recommendations for Addressing the COVID-19 Pandemic," Sustainability, MDPI, vol. 13(5), pages 1-38, March.
    7. Jialei Jiang & Eun-Mi Park & Seong-Taek Park, 2021. "The Impact of the COVID-19 on Economic Sustainability—A Case Study of Fluctuation in Stock Prices for China and South Korea," Sustainability, MDPI, vol. 13(12), pages 1-17, June.
    8. Díaz, Violeta & Ibrushi, Denada & Zhao, Jialin, 2021. "Reconsidering systematic factors during the Covid-19 pandemic – The rising importance of ESG," Finance Research Letters, Elsevier, vol. 38(C).
    9. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    10. Ascaryan Rafinda & Timea Gal, 2022. "Covid-19 Pandemic And Its Impact On Household Financial Behavior In Indonesia," Oradea Journal of Business and Economics, University of Oradea, Faculty of Economics, vol. 7(special), pages 77-85, June.
    11. Hua Song & Yudong Yang & Zheng Tao, 2020. "How different types of financial service providers support small- and medium- enterprises under the impact of COVID-19 pandemic: from the perspective of expectancy theory," Frontiers of Business Research in China, Springer, vol. 14(1), pages 1-27, December.
    12. Katarzyna Czech & Michał Wielechowski & Pavel Kotyza & Irena Benešová & Adriana Laputková, 2020. "Shaking Stability: COVID-19 Impact on the Visegrad Group Countries’ Financial Markets," Sustainability, MDPI, vol. 12(15), pages 1-19, August.
    13. Peng-Fei Dai & Xiong Xiong & Zhifeng Liu & Toan Luu Duc Huynh & Jianjun Sun, 2021. "Preventing crash in stock market: The role of economic policy uncertainty during COVID-19," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 7(1), pages 1-15, December.
    14. Islam, Raisul & Volkov, Vladimir, 2020. "Calm before the storm: an early warning approach before and during the COVID-19 crisis," Working Papers 2020-09, University of Tasmania, Tasmanian School of Business and Economics.
    15. Naes, Randi & Skjeltorp, Johannes A., 2003. "Equity trading by institutional investors: Evidence on order submission strategies," Journal of Banking & Finance, Elsevier, vol. 27(9), pages 1779-1817, September.
    16. Wang, Zhixuan & Dong, Yanli & Liu, Ailan, 2022. "How does China's stock market react to supply chain disruptions from COVID-19?," International Review of Financial Analysis, Elsevier, vol. 82(C).
    17. Ozkan, Oktay, 2021. "Impact of COVID-19 on stock market efficiency: Evidence from developed countries," Research in International Business and Finance, Elsevier, vol. 58(C).
    18. Baris Kocaarslan & Ugur Soytas, 2021. "The Asymmetric Impact of Funding Liquidity Risk on the Volatility of Stock Portfolios during the COVID-19 Crisis," Sustainability, MDPI, vol. 13(4), pages 1-12, February.
    19. Fariha Jahan & Jungmu Kim, 2023. "Does the Shield Effect of CSR Work in Crises? Evidence in Korea," Sustainability, MDPI, vol. 15(11), pages 1-18, June.
    20. Aharon, David Y. & Siev, Smadar, 2021. "COVID-19, government interventions and emerging capital markets performance," Research in International Business and Finance, Elsevier, vol. 58(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2020:i:1:p:54-:d:469927. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.