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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 forward measure ： ウィキペディア英語版 forward measure In finance, a ''T''-forward measure is a pricing measure absolutely continuous with respect to a risk-neutral measure but rather than using the money market as numeraire, it uses a bond with maturity ''T''. The use of the forward measure was pioneered by Farshid Jamshidian (1987), and later used as a means of calculating the price of options on bonds. == Mathematical definition〔Martingale methods in financial modelling. 2nd ed. New York : Springer-Verlag, 2004. Print.〕 == Let : $B(T)\; =\; \backslash exp\backslash left(\backslash int\_0^T\; r(u)\backslash ,\; du\backslash right)$ be the bank account or money market account numeraire and : $D(T)\; =\; 1/B(T)\; =\; \backslash exp\backslash left(-\backslash int\_0^T\; r(u)\backslash ,\; du\backslash right)$ be the discount factor in the market at time 0 for maturity ''T''. If $Q\_$ * is the risk neutral measure, then the forward measure $Q\_T$ is defined via the Radon–Nikodym derivative given by :$\backslash frac\; =\; \backslash frac\; =\; \backslash frac.$ Note that this implies that the forward measure and the risk neutral measure coincide when interest rates are deterministic. Also, this is a particular form of the change of numeraire formula by changing the numeraire from the money market or bank account ''B''(''t'') to a ''T''-maturity bond ''P''(''t'',''T''). Indeed, if in general :$P(t,T)\; =\; E\_\backslash left()\; =\; E\_\backslash left()$ is the price of a zero coupon bond at time ''t'' for maturity ''T'', where $\backslash mathcal(t)$ is the filtration denoting market information at time ''t'', then we can write :$\backslash frac\; =\; \backslash frac$ from which it is indeed clear that the forward ''T'' measure is associated to the ''T''-maturity zero coupon bond as numeraire. For a more detailed discussion see Brigo and Mercurio (2001). 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「forward measure」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.