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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 SABR volatility model ： ウィキペディア英語版 SABR volatility model In mathematical finance, the SABR model is a stochastic volatility model, which attempts to capture the volatility smile in derivatives markets. The name stands for "stochastic alpha, beta, rho", referring to the parameters of the model. The SABR model is widely used by practitioners in the financial industry, especially in the interest rate derivative markets. It was developed by Patrick S. Hagan, Deep Kumar, Andrew Lesniewski, and Diana Woodward. == Dynamics == The SABR model describes a single forward $F$, such as a LIBOR forward rate, a forward swap rate, or a forward stock price. The volatility of the forward $F$ is described by a parameter $\backslash sigma$. SABR is a dynamic model in which both $F$ and $\backslash sigma$ are represented by stochastic state variables whose time evolution is given by the following system of stochastic differential equations: :$dF\_t=\backslash sigma\_t\; F^\backslash beta\_t\backslash ,\; dW\_t,$ :$d\backslash sigma\_t=\backslash alpha\backslash sigma^\{\}\_t\backslash ,\; dZ\_t,$ with the prescribed time zero (currently observed) values $F\_0$ and $\backslash sigma\_0$. Here, $W\_t$ and $Z\_t$ are two correlated Wiener processes with correlation coefficient : :$dW\_t\; dZ\_t\; =\; \backslash rho\; dt$ The constant parameters $\backslash beta,\backslash ;\backslash alpha$ satisfy the conditions $0\backslash leq\backslash beta\backslash leq\; 1,\backslash ;\backslash alpha\backslash geq\; 0$. The above dynamics is a stochastic version of the CEV model with the ''skewness'' parameter $\backslash beta$: in fact, it reduces to the CEV model if $\backslash alpha=0$ The parameter $\backslash alpha$ is often referred to as the ''volvol'', and its meaning is that of the lognormal volatility of the volatility parameter $\backslash sigma$. 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「SABR volatility 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.