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

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 parame...