A New Option Model Prices Stocks with Market History and ESG Ratings

A stock option is not just a bet on where a price ends up; it is also a bet on how the road gets there. This paper builds a pricing model that lets the history of a market index affect stock price changes, while also folding in an ESG rating, or environmental, social, and governance score, through a single adjustable parameter. The authors extend a unified Bachelier-Black-Scholes-Merton model and turn it into a discrete binary tree for pricing European call options. They test the model on 10 stocks from the Nasdaq-100, fit it to stock price changes, and compare the model-based prices with published European call option prices. The result is a framework designed to capture both path dependence and ESG influence in one place, giving researchers a way to study how market history and sustainability signals can shape valuation.

Ten Nasdaq-100 stocks anchor this test. Their option prices do not only depend on where the stock ends. This model also asks how the price got there. That matters because two paths can share one finish line. One path can be calm. Another can lurch and recover. A trader may care about both. The paper folds that history into a unified price model. It also adds ESG, which means environmental, social, and governance rating. One adjustable parameter controls how much that rating changes value. The result is a price story with memory, not just a snapshot. That makes valuation feel less like a photo and more like a film. If the path changes, the price can change with it.

When a stock remembers its path

Path dependence is the big shift here. The model extends the Cherny-Shiryaev-Yor invariance principle, a math bridge from steps to smooth motion. It places that bridge inside the unified Bachelier-Black-Scholes-Merton frame. Bachelier treats price moves in dollars. Black-Scholes-Merton treats them as percent moves. The unified form keeps both ideas in one frame. From there, a binary tree prices European call options, which give the right to buy later. A binary tree is a step-by-step map with up and down branches. The setup fits stock price changes for 10 Nasdaq-100 names. It compares model prices with published European call prices. That lets the setup test whether market memory and ESG can travel together.

How the new tree is built

Start with the market index. Let its past moves shape the next stock move. Add ESG as part of the risky asset, which means the stock that can lose value. One parameter controls the ESG effect. Move that knob, and the ESG influence grows or fades. The pricing engine then builds a binary tree. Each branch gives an up move or a down move. The tree uses the unified Bachelier-Black-Scholes-Merton rules. Those rules let the model sit between the older Bachelier and Black-Scholes worlds. In plain terms, the model can speak both dollar changes and percent changes.

Why the extra knobs matter

This matters because valuation often strips away context. A plain price tag can hide the route that made it. This setup keeps that route in view. It also gives ESG a clear place in the math. ESG no longer sits as a vague label on the side. It becomes a tunable part of stock value. That makes the model useful for a sharper question. How much should market memory count? How much should ESG count? The answer now lives in one parameter, not in two separate tools. It can help compare cases with the same price and different paths. It can also show how much ESG shifts the final valuation.

What to test next

The next test is larger than 10 stocks. It is the rest of the Nasdaq-100. The same setup also needs fresh market swings and fresh ESG scores. If it keeps matching published European call prices, the model gains real pull. It becomes one place to study two forces at once. It can track the market's memory. It can also test how much a rating changes value. A stock option does not have to be only a bet on the finish line. It can also be a bet on the path.