The Black-Scholes model, also known as the Black-Scholes-Merton (BSM) model, is a widely used mathematical formula to price European-style options contracts. The model was first introduced in 1973 by Fisher Black, Myron Scholes, and Robert Merton and has become the cornerstone of all modern options pricing theory. It is also considered one of the most successful of all financial models due to its practical application and accuracy.

In order to accurately price an option, the Black-Scholes model requires five primary inputs which include the strike price of an option, the current stock price, the time to expiration, the risk-free rate, and the volatility. The strike price is the price at which an option may be exercised, while the current stock price is the price at which the underlying security (typically a stock) is currently trading. The time to expiration is the length of time until the option’s expiration date and is typically quoted in days, while the risk-free rate is the current rate of return on an investment that has no risk. Finally, the volatility of the security is the estimated standard deviation associated with the stock’s daily average price return.

Once the five input variables are known, the Black-Scholes model then uses a differential equation to calculate the theoretical price of a European style option and determine if it should be a “call option” or a “put option.” A call option is a contract that gives the buyer the right, but not the obligation, to buy a security at a specified price at a future date, while a put option is a similar contract that gives the buyer the right, but not the obligation, to sell a security at a specified price at a future date.

Though usually accurate in predicting the price of an option, the Black-Scholes model is not perfect and assumptions that are used in deriving the equation can cause predictions to deviate from real-world results. In addition, the model is only used to price European options, as the model does not take into consideration the fact that American options could be exercised before the expiration date.

Since its introduction in 1973, the Black-Scholes model has become the cornerstone in the pricing of options and has greatly increased the popularity of options trading. With its practical application and empirical accuracy, the Black-Scholes model remains one of the most successful and influential models in financial history.