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Exploring Dynamic Asset Pricing within Bachelier’s Market Model

Author

Listed:
  • Nancy Asare Nyarko

    (Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042, USA)

  • Bhathiya Divelgama

    (Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042, USA)

  • Jagdish Gnawali

    (Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042, USA)

  • Blessing Omotade

    (Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042, USA)

  • Svetlozar T. Rachev

    (Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042, USA)

  • Peter Yegon

    (Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042, USA)

Abstract

This paper delves into the dynamics of asset pricing within Bachelier’s market model (BMM), elucidating the representation of risky asset price dynamics and the definition of riskless assets. It highlights the fundamental differences between BMM and the Black–Scholes–Merton market model (BSMMM), including the extension of BMM to handle assets yielding a simple dividend. Our investigation further explores Bachelier’s term structure of interest rates (BTSIR), introducing a novel version of Bachelier’s Heath–Jarrow–Morton model and adapting the Hull–White interest rate model to fit BMM. This study concludes by examining the applicability of BMM in real-world scenarios, such as those involving environmental, social, and governance (ESG)-adjusted stock prices and commodity spreads.

Suggested Citation

  • Nancy Asare Nyarko & Bhathiya Divelgama & Jagdish Gnawali & Blessing Omotade & Svetlozar T. Rachev & Peter Yegon, 2023. "Exploring Dynamic Asset Pricing within Bachelier’s Market Model," JRFM, MDPI, vol. 16(8), pages 1-18, July.
    • Handle: RePEc:gam:jjrfmx:v:16:y:2023:i:8:p:352-:d:1203273
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    References listed on IDEAS

    as
    1. Davide Lauria & W. Brent Lindquist & Stefan Mittnik & Svetlozar T. Rachev, 2022. "ESG-Valued Portfolio Optimization and Dynamic Asset Pricing," Papers 2206.02854, arXiv.org.
    2. Schaefer, Matthew P., 2002. "Pricing And Hedging European Options On Futures Spreads Using The Bachelier Spread Option Model," 2002 Conference, April 22-23, 2002, St. Louis, Missouri 19055, NCR-134 Conference on Applied Commodity Price Analysis, Forecasting, and Market Risk Management.
    3. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    4. Yuan Hu & W. Brent Lindquist & Svetlozar T. Rachev, 2022. "ESG-valued discrete option pricing in complete markets," Papers 2209.06276, arXiv.org.
    5. Hull, John & White, Alan, 1993. "One-Factor Interest-Rate Models and the Valuation of Interest-Rate Derivative Securities," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 28(2), pages 235-254, June.
    6. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
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