The Black-Scholes model, published in 1973 by Fischer Black and Myron Scholes (with key contributions from Robert Merton), was one of the most consequential developments in financial economics. It provided, for the first time, a closed-form formula for pricing European options — calls and puts on an underlying asset with a defined expiry and strike.
What Black-Scholes does
The model takes five inputs — the current price of the underlying, the option's strike price, time to expiry, the risk-free interest rate, and the expected volatility of the underlying — and produces the fair value of a European option. Equally important, it provides the delta: the hedge ratio telling you how much underlying to hold to create a risk-neutral position.
This was revolutionary because it showed that options could be priced using dynamic hedging — continuously adjusting a portfolio of the underlying to replicate the option's payoff profile. The insight that options were not simply bets on direction but replicable claims transformed derivatives markets.
The assumptions and why they fail
Black-Scholes rests on several assumptions that do not hold in practice: constant volatility (implied volatility is not constant — it varies by strike and maturity, creating the 'volatility smile' and 'volatility surface'); continuous trading without transaction costs; normally distributed returns (actual returns have fat tails — large moves occur far more frequently than a normal distribution predicts); and no jumps (asset prices can gap, especially around events like earnings or central bank decisions).
Why it is still used
Despite its limitations, Black-Scholes remains the industry standard quotation convention. Options are not quoted in dollar terms — they are quoted in implied volatility: the volatility that, when plugged into the Black-Scholes formula, produces the observed market price. This standardisation allows traders to compare options across strikes and maturities on a common scale.