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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Vasicek model ： ウィキペディア英語版 Vasicek model In finance, the Vasicek model is a mathematical model describing the evolution of interest rates. It is a type of one-factor short rate model as it describes interest rate movements as driven by only one source of market risk. The model can be used in the valuation of interest rate derivatives, and has also been adapted for credit markets, although its use in the credit market is in principle wrong, implying negative probabilities (see for example Brigo and Mercurio (2006), Section 21.1.1). It was introduced in 1977 by Oldřich Vašíček〔 〕 and can be also seen as a stochastic investment model. ==Details== The model specifies that the instantaneous interest rate follows the stochastic differential equation: :$dr\_t\; =\; a(b-r\_t)\backslash ,\; dt\; +\; \backslash sigma\; \backslash ,\; dW\_t$ where ''Wt'' is a Wiener process under the risk neutral framework modelling the random market risk factor, in that it models the continuous inflow of randomness into the system. The standard deviation parameter, $\backslash sigma$, determines the volatility of the interest rate and in a way characterizes the amplitude of the instantaneous randomness inflow. The typical parameters $b,\; a$ and $\backslash sigma$, together with the initial condition $r\_0$, completely characterize the dynamics, and can be quickly characterized as follows, assuming $a$ to be non-negative: * $b$: "long term mean level". All future trajectories of $r$ will evolve around a mean level b in the long run; * $a$: "speed of reversion". $a$ characterizes the velocity at which such trajectories will regroup around $b$ in time; * $\backslash sigma$: "instantaneous volatility", measures instant by instant the amplitude of randomness entering the system. Higher $\backslash sigma$ implies more randomness The following derived quantity is also of interest, * $/(2\; a)$: "long term variance". All future trajectories of $r$ will regroup around the long term mean with such variance after a long time. $a$ and $\backslash sigma$ tend to oppose each other: increasing $\backslash sigma$ increases the amount of randomness entering the system, but at the same time increasing $a$ amounts to increasing the speed at which the system will stabilize statistically around the long term mean $b$ with a corridor of variance determined also by $a$. This is clear when looking at the long term variance, :$\backslash frac$ which increases with $\backslash sigma$ but decreases with $a$. This model is an Ornstein–Uhlenbeck stochastic process. Making the long term mean stochastic to another SDE is a simplified version of the cointelation SDE. 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「Vasicek model」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.