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A short-rate model, in the context of interest rate derivatives, is a mathematical model that describes the future evolution of interest rates by describing the future evolution of the short rate, usually written . ==The short rate== Under a short rate model, the stochastic state variable is taken to be the instantaneous spot rate.〔(''Short rate models'' ), Prof. Andrew Lesniewski, NYU〕 The short rate, , then, is the (continuously compounded, annualized) interest rate at which an entity can borrow money for an infinitesimally short period of time from time . Specifying the current short rate does not specify the entire yield curve. However no-arbitrage arguments show that, under some fairly relaxed technical conditions, if we model the evolution of as a stochastic process under a risk-neutral measure then the price at time of a zero-coupon bond maturing at time with a payoff of 1 is given by : where is the natural filtration for the process. The interest rates implied by the zero coupon bonds form a yield curve or more precisely, a zero curve. Thus specifying a model for the short rate specifies future bond prices. This means that instantaneous forward rates are also specified by the usual formula : 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「Short-rate model」の詳細全文を読む スポンサード リンク
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