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

Bhathiya Divelgama, Nancy Asare Nyarko, W. Brent Lindquist, Svetlozar T. Rachev and Blessing Omotade

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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.

Date: 2025-08
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