Black–Scholes equation

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In mathematical finance, the Black–Scholes equation, also called the Black–Scholes–Merton equation, is a partial differential equation (PDE) governing the price evolution of derivatives under the Black–Scholes model. Broadly speaking, the term may refer to a similar PDE that can be derived for a variety of options, or more generally, derivatives. Consider a stock paying no dividends. Now construct any derivative that has a fixed maturation time T {\displaystyle T} in the future, and at maturation, it has payoff K ( S T ) {\displaystyle K(S_{T})} that depends on the values taken by the stock at that moment (such as European call or put options). Then the price of the derivative satisfies {...

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