The Black-Scholes formula is the result obtained by solving the partial differential equation that must be satisfied within the Black-Scholes model of an equity's price. The formula gives the price of a European call option by taking into account the price of the underlying stock, the volatility of the underlying, the time value of money, and the time remaining before the option expires. The price for a corresponding European put option can be derived from the solution to the Black-Scholes formula using put-call parity. Also, the Greeks are calculated from this model. The Black-Scholes model of an equity's price, on which the formula is based, assumes that an equity's price follows a geometric Brownian motion with a constant drift and constant volatility.
The Black-Scholes model for option pricing was first published by Robert C. Merton in 1973. Merton's model expanded on the previous work of Fischer Black and Myron Scholes. The Black-Scholes model/formula is still widely used for computing fair option prices today and for their achievement Merton and Scholes won the Nobel Prize in Economics in 1997. Fischer Black was officially recognized as a contributor to the work as he was ineligible to receive the prize on account of his death in 1995.