Black-Scholes priced options by hedging away risk, and a derivative market was born

Before 1973, pricing an option meant taking a view on the stock's expected return and on how much risk premium investors demanded. Earlier attempts from Louis Bachelier onward all stumbled on that risk premium, which depends on unobservable attitudes toward risk.

The breakthrough was the discovery that the risk premium is already inside the stock price. An investor can build a portfolio of the stock and options that is risk-free, and must continuously adjust its composition as time passes. A risk-free portfolio must earn the risk-free interest rate, so the option's fair value is forced by arbitrage—no opinion about the future direction of the stock is needed.

In 1973 Black and Scholes published the resulting formula, and Merton supplied a more general derivation. The formula needs only the current stock price, strike price, volatility, time to maturity and the risk-free rate. Thousands of traders use it daily, and it became the foundation of the derivatives markets that grew rapidly over the following decades.

Hedge the option away; its price follows from arbitrage

The replicating-portfolio argument removed the unobservable risk premium that had blocked every earlier attempt.

Arbitrage enforces the formula: if price and formula disagree, a risk-free profit exists, so traders push prices back.

The formula is computable in seconds from five observable inputs, so it could actually be used on a trading floor.

Merton's general derivation extended the method far beyond stock options, to guarantees, insurance and project flexibility.

If you can hedge away the risk of a product, you no longer need to guess a risk premium—the market price follows from the hedge itself.

Merton and Scholes received the 1997 Nobel Prize in Economic Sciences for the method, in collaboration with the late Fischer Black. Derivatives markets grew explosively; the formula and its descendants became standard in exchanges worldwide, and its logic spread to pricing insurance contracts, guarantees and real investment options.