Black-Scholes-Merton model
Principles of Finance glossary · Risk, Return & Portfolio Theory
Definition
The continuous-time option pricing model that yields closed-form formulas for European options on lognormally distributed underlyings.
Black-Scholes-Merton model in plain English
This is the famous formula that finally gave the world a clean, exact price for a stock option, and it won a Nobel Prize. Instead of the binomial model's discrete up-or-down flips, it imagines the stock price wiggling smoothly and continuously every instant, and it assumes those wiggles follow a specific bell-curve-like pattern (so the price can drift but never goes negative). The payoff is a plug-and-chug equation: feed in the stock price, the strike, time left, interest rate, and how jumpy the stock is, and out pops the option's value — no simulation needed. It only handles 'European' options (ones you can exercise solely at the end), but it's the bedrock that modern derivatives markets were built on.
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