IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2509.18099.html
   My bibliography  Save this paper

Path-dependent, ESG-valued, option pricing in the Bachelier-Black-Scholes-Merton model

Author

Listed:
  • Bhathiya Divelgama
  • Nancy Asare Nyarko
  • W. Brent Lindquist
  • Svetlozar T. Rachev
  • Blessing Omotade

Abstract

We extend the application of the Cherny-Shiryaev-Yor invariance principle to a unified Bachelier-Black-Scholes-Merton (BBSM) dynamic pricing model. This extension incorporates the influence of the history of the dynamics (i.e., the path dynamics) of a market index on stock price changes. We add an ESG rating component to the price of the risky asset (stock), in such a manner that the impact of the ESG rating on the stock valuation can be explored through variation in the value of a single parameter. We develop discrete, binary tree, option pricing under this extended model. Using an empirical data set of 10 stocks chosen from the Nasdaq-100, we fit the model to stock price changes and compare model-based and published European call option prices.

Suggested Citation

  • Bhathiya Divelgama & Nancy Asare Nyarko & W. Brent Lindquist & Svetlozar T. Rachev & Blessing Omotade, 2025. "Path-dependent, ESG-valued, option pricing in the Bachelier-Black-Scholes-Merton model," Papers 2509.18099, arXiv.org.
    • Handle: RePEc:arx:papers:2509.18099
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2509.18099
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Pástor, Ľuboš & Stambaugh, Robert F. & Taylor, Lucian A., 2021. "Sustainable investing in equilibrium," Journal of Financial Economics, Elsevier, vol. 142(2), pages 550-571.
    3. W. Brent Lindquist & Svetlozar T. Rachev & Jagdish Gnawali & Frank J. Fabozzi, 2024. "Dynamic Asset Pricing in a Unified Bachelier–Black–Scholes–Merton Model," Risks, MDPI, vol. 12(9), pages 1-24, August.
    4. Robert Brooks & Joshua A. Brooks, 2017. "An Option Valuation Framework Based On Arithmetic Brownian Motion: Justification And Implementation Issues," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 40(3), pages 401-427, September.
    5. Yuan Hu & Abootaleb Shirvani & W. Brent Lindquist & Frank J. Fabozzi & Svetlozar T. Rachev, 2020. "Option Pricing Incorporating Factor Dynamics in Complete Markets," JRFM, MDPI, vol. 13(12), pages 1-33, December.
    6. Yuan Hu & Abootaleb Shirvani & Stoyan Stoyanov & Young Shin Kim & Frank J. Fabozzi & Svetlozar T. Rachev, 2020. "Option Pricing in Markets with Informed Traders," Papers 2006.02596, arXiv.org, revised Aug 2020.
    7. Jaehyuk Choi & Minsuk Kwak & Chyng Wen Tee & Yumeng Wang, 2021. "A Black-Scholes user's guide to the Bachelier model," Papers 2104.08686, arXiv.org, revised Feb 2022.
    8. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    9. Yuan Hu & Abootaleb Shirvani & Stoyan Stoyanov & Young Shin Kim & Frank J. Fabozzi & Svetlozar T. Rachev, 2020. "Option Pricing In Markets With Informed Traders," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(06), pages 1-32, September.
    10. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    11. Nancy Asare Nyarko & Bhathiya Divelgama & Jagdish Gnawali & Blessing Omotade & Svetlozar Rachev & Peter Yegon, 2023. "Exploring Dynamic Asset Pricing within Bachelier Market Model," Papers 2307.04059, arXiv.org.
    12. Pedersen, Lasse Heje & Fitzgibbons, Shaun & Pomorski, Lukasz, 2021. "Responsible investing: The ESG-efficient frontier," Journal of Financial Economics, Elsevier, vol. 142(2), pages 572-597.
    13. W. Brent Lindquist & Svetlozar T. Rachev & Jagdish Gnawali & Frank J. Fabozzi, 2024. "Dynamic Asset Pricing in a Unified Bachelier-Black-Scholes-Merton Model," Papers 2405.12479, arXiv.org, revised Jun 2024.
    14. Walter Schachermayer & Josef Teichmann, 2008. "How Close Are The Option Pricing Formulas Of Bachelier And Black–Merton–Scholes?," Mathematical Finance, Wiley Blackwell, vol. 18(1), pages 155-170, January.
    15. Davide Lauria & W. Brent Lindquist & Stefan Mittnik & Svetlozar T. Rachev, 2025. "Environmental, Social and Governance-Valued Portfolio Optimization and Dynamic Asset Pricing," JRFM, MDPI, vol. 18(3), pages 1-33, March.
    16. Olivier David Zerbib, 2022. "A Sustainable Capital Asset Pricing Model (S-CAPM): Evidence from Environmental Integration and Sin Stock Exclusion [Asset pricing with liquidity risk]," Review of Finance, European Finance Association, vol. 26(6), pages 1345-1388.
    17. Jaehyuk Choi & Minsuk Kwak & Chyng Wen Tee & Yumeng Wang, 2022. "A Black–Scholes user's guide to the Bachelier model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(5), pages 959-980, May.
    18. Yuan Hu & W. Brent Lindquist & Svetlozar T. Rachev, 2025. "Sustainability-valued discrete option pricing in complete markets," Journal of Sustainable Finance & Investment, Taylor & Francis Journals, vol. 15(2), pages 403-437, April.
    19. Svetlozar Rachev & Nancy Asare Nyarko & Blessing Omotade & Peter Yegon, 2024. "Bachelier’s Market Model for ESG Asset Pricing," JRFM, MDPI, vol. 17(12), pages 1-23, December.
    20. Yuan Hu & Abootaleb Shirvani & W. Brent Lindquist & Frank J. Fabozzi & Svetlozar T. Rachev, 2020. "Option Pricing Incorporating Factor Dynamics in Complete Markets," Papers 2011.08343, arXiv.org.
    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. W. Brent Lindquist & Svetlozar T. Rachev & Jagdish Gnawali & Frank J. Fabozzi, 2024. "Dynamic Asset Pricing in a Unified Bachelier-Black-Scholes-Merton Model," Papers 2405.12479, arXiv.org, revised Jun 2024.
    2. Hu, Yuan & Lindquist, W. Brent & Rachev, Svetlozar T. & Shirvani, Abootaleb & Fabozzi, Frank J., 2022. "Market complete option valuation using a Jarrow-Rudd pricing tree with skewness and kurtosis," Journal of Economic Dynamics and Control, Elsevier, vol. 137(C).
    3. W. Brent Lindquist & Svetlozar T. Rachev, 2025. "Alternatives to classical option pricing," Annals of Operations Research, Springer, vol. 346(1), pages 489-509, March.
    4. Davide Lauria & W. Brent Lindquist & Svetlozar T. Rachev & Yuan Hu, 2023. "Unifying Market Microstructure and Dynamic Asset Pricing," Papers 2304.02356, arXiv.org, revised Feb 2024.
    5. Yuan Hu & Abootaleb Shirvani & W. Brent Lindquist & Frank J. Fabozzi & Svetlozar T. Rachev, 2021. "Market Complete Option Valuation using a Jarrow-Rudd Pricing Tree with Skewness and Kurtosis," Papers 2106.09128, arXiv.org.
    6. Jaehyuk Choi & Minsuk Kwak & Chyng Wen Tee & Yumeng Wang, 2022. "A Black–Scholes user's guide to the Bachelier model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(5), pages 959-980, May.
    7. Yuan Hu & Abootaleb Shirvani & W. Brent Lindquist & Frank J. Fabozzi & Svetlozar T. Rachev, 2020. "Option Pricing Incorporating Factor Dynamics in Complete Markets," Papers 2011.08343, arXiv.org.
    8. Yuan Hu & W. Brent Lindquist & Svetlozar T. Rachev & Frank J. Fabozzi, 2023. "Option pricing using a skew random walk pricing tree," Papers 2303.17014, arXiv.org.
    9. Eden Gross & Ryan Kruger & Francois Toerien, 2025. "A comparative analysis of option pricing models: Black–Scholes, Bachelier, and artificial neural networks," Risk Management, Palgrave Macmillan, vol. 27(2), pages 1-16, May.
    10. W. Brent Lindquist & Svetlozar T. Rachev, 2024. "Alternatives to classical option pricing," Papers 2403.17187, arXiv.org.
    11. Benchora, Inessa & Leroy, Aurélien & Raffestin, Louis, 2025. "Is monetary policy transmission green?," Economic Modelling, Elsevier, vol. 144(C).
    12. Davide Lauria & W. Brent Lindquist & Svetlozar T. Rachev & Yuan Hu, 2025. "Bridging Asset Pricing and Market Microstructure: Option Valuation in Roll’s Framework," JRFM, MDPI, vol. 18(5), pages 1-43, April.
    13. Daniel Guterding, 2023. "Sparse Modeling Approach to the Arbitrage-Free Interpolation of Plain-Vanilla Option Prices and Implied Volatilities," Risks, MDPI, vol. 11(5), pages 1-24, April.
    14. Pástor, Ľuboš & Stambaugh, Robert F. & Taylor, Lucian A., 2022. "Dissecting green returns," Journal of Financial Economics, Elsevier, vol. 146(2), pages 403-424.
    15. Alessi, Lucia & Ossola, Elisa & Panzica, Roberto, 2023. "When do investors go green? Evidence from a time-varying asset-pricing model," International Review of Financial Analysis, Elsevier, vol. 90(C).
    16. Covachev, Svetoslav & Martel, Jocelyn & Brito-Ramos, Sofia, 2025. "Are ESG factors truly unique?," The North American Journal of Economics and Finance, Elsevier, vol. 77(C).
    17. Hambel, Christoph & van der Ploeg, Frederick, 2025. "Policy transition risk, carbon premiums, and asset prices," Journal of Monetary Economics, Elsevier, vol. 152(C).
    18. Alexander Lipton, 2024. "Hydrodynamics of Markets:Hidden Links Between Physics and Finance," Papers 2403.09761, arXiv.org.
    19. Fricke, Daniel & Meinerding, Christoph, 2025. "Who pays the greenium and why? A decomposition," Journal of International Money and Finance, Elsevier, vol. 157(C).
    20. Quaye, Enoch & Tunaru, Diana & Tunaru, Radu, 2024. "Green-adjusted share prices: A comparison between standard investors and investors with green preferences," Journal of Financial Stability, Elsevier, vol. 74(C).

    More about this item

    Statistics

    Access and download statistics

    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:arx:papers:2509.18099. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.