An equation used to value financial options. The Black–Scholes equation is based on a model of equilibrium in financial markets with continuous trading. That is, asset prices potentially change at every instant in time. The model assumes that there is a risk-free asset and that all excess returns are eliminated by arbitrage. The method of Black–Scholes is to develop a partial differential equation that the price of every option must satisfy. This equation states that the value, V, of an option must satisfy
where S is the value at time t of the underlying asset, r is the risk-free rate of return, and σ2 is the variance of the return on the underlying asset. The value of a particular option is found by solving the partial differential equation using as boundary conditions the characteristics of that option.