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

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  • 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
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