Black-Scholes Model

The model was published in 1973 by economists Fischer Black and Myron Scholes, with important contributions from Robert Merton. Scholes and Merton received the Nobel Prize in Economics in 1997; Black had died in 1995.

The model’s key insight is that an option’s risk can be hedged by holding the right amount of the underlying asset, so its price can be calculated without knowing investors’ attitudes to risk. The formula requires five main inputs: the current price of the underlying, the exercise price, the time until expiry, the risk-free interest rate and the expected volatility of the underlying.

For example, traders can use the model to estimate the value of a call option on a share, or work backwards from an option’s market price to find its implied volatility.

The model rests on simplifying assumptions, such as constant volatility, continuous trading, no transaction costs and returns that follow a lognormal distribution. Real markets do not meet these assumptions, which helps explain volatility skew. Despite its limits, Black-Scholes transformed options markets and remains a foundation of financial theory.