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A local volatility model, in mathematical finance and financial engineering, is one that treats volatility as a function of both the current asset level and of time . As such, a local volatility model is a generalisation of the Black-Scholes model, where the volatility is a constant (i.e. a trivial function of and ). ==Formulation== In mathematical finance, the asset ''S''''t'' that underlies a financial derivative, is typically assumed to follow a stochastic differential equation of the form :, where is the instantaneous risk free rate, giving an average local direction to the dynamics, and is a Wiener process, representing the inflow of randomness into the dynamics. The amplitude of this randomness is measured by the instant volatility . In the simplest model i.e. the Black-Scholes model, is assumed to be constant; in reality, the realized volatility of an underlying actually varies with time. When such volatility has a randomness of its own—often described by a different equation driven by a different ''W''—the model above is called a stochastic volatility model. And when such volatility is merely a function of the current asset level ''S''''t'' and of time ''t'', we have a local volatility model. The local volatility model is a useful simplification of the stochastic volatility model. "Local volatility" is thus a term used in quantitative finance to denote the set of diffusion coefficients, , that are consistent with market prices for all options on a given underlying. This model is used to calculate exotic option valuations which are consistent with observed prices of vanilla options. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「local volatility」の詳細全文を読む スポンサード リンク
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