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

2025/08/26 by Divelgama, Bhathiya, Nyarko, Nancy Asare, Lindquist, W. Brent +2
#FOS: Economics and business #Pricing of Securities (q-fin.PR)

paper · doi:10.48550/arxiv.2509.18099

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.

Citations

• Dynamic Asset Pricing in a Unified Bachelier-Black-Scholes-Merton Model
• Exploring Dynamic Asset Pricing within Bachelier Market Model
• Bachelier's Market Model for ESG Asset Pricing
• Option Pricing Incorporating Factor Dynamics in Complete Markets
• How close are the option pricing formulas of Bachelier and Black-Merton-Scholes?
• On a non-classical invariance principle
• The Pricing of Options and Corporate Liabilities

Related

• Bachelier's Market Model for ESG Asset Pricing
• Option Pricing Incorporating Factor Dynamics in Complete Markets
• Option pricing: A yet simpler approach
• ESG-valued discrete option pricing in complete markets
• A derivation of the Black-Scholes option pricing model using a central limit theorem argument