Black-Scholes model

The Black-Scholes model, sometimes called the Black-Scholes-Merton model, is a mathematical model for the dynamics of a financial market that contains derivative investment instruments such as options. From its central partial differential equation, the Black-Scholes equation, one can derive the Black-Scholes formula, which gives a theoretical price for European-style options based on the risk of the underlying security and its expected return. The model is named for economists Fischer Black and Myron Scholes, with Robert C. Merton, who first wrote an academic paper extending the idea, sometimes also credited. Its central technique is to hedge the option by continuously buying and selling the underlying asset in a way designed to eliminate risk, an approach called continuously revised delta hedging, and although its assumptions have since been relaxed and generalized in many directions, the model remains widely used, often with adjustments, by options market participants.