“Black–Scholes equation”的概念、定义、翻译、参考文献-科学参考

Black–Scholes equation

Economics

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

$\frac{\partial V}{\partial t} + \frac{1}{2} σ^{2} S^{2} \frac{\partial^{2} V}{\partial S^{2}} + r S \frac{\partial V}{\partial S} - r V = 0$

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.

单词	Black–Scholes equation
释义	Black–Scholes equation Economics 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 $\frac{\partial V}{\partial t} + \frac{1}{2} σ^{2} S^{2} \frac{\partial^{2} V}{\partial S^{2}} + r S \frac{\partial V}{\partial S} - r V = 0$ 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.
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