翻訳と辞書 Words near each other ・ "O" Is for Outlaw ・ "O"-Jung.Ban.Hap. ・ "Ode-to-Napoleon" hexachord ・ "Oh Yeah!" Live ・ "Our Contemporary" regional art exhibition (Leningrad, 1975) ・ "P" Is for Peril ・ "Pimpernel" Smith ・ "Polish death camp" controversy ・ "Pro knigi" ("About books") ・ "Prosopa" Greek Television Awards ・ "Pussy Cats" Starring the Walkmen ・ "Q" Is for Quarry ・ "R" Is for Ricochet ・ "R" The King (2016 film) ・ "Rags" Ragland ・ ! (album) ・ ! (disambiguation) ・ !! ・ !!! ・ !!! (album) ・ !!Destroy-Oh-Boy!! ・ !Action Pact! ・ !Arriba! La Pachanga ・ !Hero ・ !Hero (album) ・ !Kung language ・ !Oka Tokat ・ !PAUS3 ・ !T.O.O.H.! ・ !Women Art Revolution Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク stochastic volatility ： ウィキペディア英語版 stochastic volatility Stochastic volatility models are those in which the variance of a stochastic process is itself randomly distributed.〔Gatheral, J. (2006). The volatility surface: a practitioner's guide. Wiley.〕 They are used in the field of mathematical finance to evaluate derivative securities, such as options. The name derives from the models' treatment of the underlying security's volatility as a random process, governed by state variables such as the price level of the underlying security, the tendency of volatility to revert to some long-run mean value, and the variance of the volatility process itself, among others. Stochastic volatility models are one approach to resolve a shortcoming of the Black–Scholes model. In particular, models based on Black-Scholes assume that the underlying volatility is constant over the life of the derivative, and unaffected by the changes in the price level of the underlying security. However, these models cannot explain long-observed features of the implied volatility surface such as volatility smile and skew, which indicate that implied volatility does tend to vary with respect to strike price and expiry. By assuming that the volatility of the underlying price is a stochastic process rather than a constant, it becomes possible to model derivatives more accurately. ==Basic model== Starting from a constant volatility approach, assume that the derivative's underlying asset price follows a standard model for geometric Brownian motion: :$dS\_t\; =\; \backslash mu\; S\_t\backslash ,dt\; +\; \backslash sigma\; S\_t\backslash ,dW\_t\; \backslash ,$ where $\backslash mu\; \backslash ,$ is the constant drift (i.e. expected return) of the security price $S\_t\; \backslash ,$, $\backslash sigma\; \backslash ,$ is the constant volatility, and $dW\_t\; \backslash ,$ is a standard Wiener process with zero mean and unit rate of variance. The explicit solution of this stochastic differential equation is :$S\_t=\; S\_0\; e^\; \backslash sigma^2)\; t+\; \backslash sigma\; W\_t\}$. The Maximum likelihood estimator to estimate the constant volatility $\backslash sigma\; \backslash ,$ for given stock prices $S\_t\; \backslash ,$ at different times $t\_i\; \backslash ,$ is : & = \frac 1 n \sum_^n (t_i-t_)\left(\frac}}}}}\right)^2;\end its expectation value is $E\; \backslash left(\backslash sigma^2\backslash right)=\; \backslash frac\; \backslash hat^2$. This basic model with constant volatility $\backslash sigma\; \backslash ,$ is the starting point for non-stochastic volatility models such as Black–Scholes model and Cox–Ross–Rubinstein model. For a stochastic volatility model, replace the constant volatility $\backslash sigma\; \backslash ,$ with a function $\backslash nu\_t\; \backslash ,$, that models the variance of $S\_t\; \backslash ,$. This variance function is also modeled as Brownian motion, and the form of $\backslash nu\_t\; \backslash ,$ depends on the particular SV model under study. :$dS\_t\; =\; \backslash mu\; S\_t\backslash ,dt\; +\; \backslash sqrt\; S\_t\backslash ,dW\_t\; \backslash ,$ :$d\backslash nu\_t\; =\; \backslash alpha\_\backslash ,dt\; +\; \backslash beta\_\backslash ,dB\_t\; \backslash ,$ where $\backslash alpha\_\; \backslash ,$ and $\backslash beta\_\; \backslash ,$ are some functions of $\backslash nu\; \backslash ,$ and $dB\_t\; \backslash ,$ is another standard gaussian that is correlated with $dW\_t\; \backslash ,$ with constant correlation factor $\backslash rho\; \backslash ,$. 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「stochastic volatility」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.