翻訳と辞書 Words near each other ・ Library and Archives Canada ・ Library and Information Association of South Africa ・ Library and information science ・ Library and Information Science Abstracts ・ Library and Information Science Access Midwest Program ・ Library and information scientist ・ Library and Information Technology Association ・ Library and Laboratory Building-Henderson Institute ・ Library angel ・ Library anxiety ・ Library assessment ・ Library Associates Companies ・ Library association ・ Libor Kozák ・ Libor Malina ・ LIBOR market model ・ Libor Michálek ・ Libor Nováček ・ Libor Němeček ・ Libor Pala ・ Libor Pešek ・ Libor Pimek ・ Libor Pivko ・ Libor Polášek ・ Libor Procházka ・ Libor Radimec ・ Libor Rouček ・ Libor scandal ・ Libor Sionko ・ Libor Sovadina 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 LIBOR market model ： ウィキペディア英語版 LIBOR market model The LIBOR market model, also known as the BGM Model (Brace Gatarek Musiela Model, in reference to the names of some of the inventors) is a financial model of interest rates.〔M. Musiela, M. Rutkowski: Martingale methods in financial modelling. 2nd ed. New York : Springer-Verlag, 2004. Print.〕 It is used for pricing interest rate derivatives, especially exotic derivatives like Bermudan swaptions, ratchet caps and floors, target redemption notes, autocaps, zero coupon swaptions, constant maturity swaps and spread options, among many others. The quantities that are modeled, rather than the short rate or instantaneous forward rates (like in the Heath-Jarrow-Morton framework) are a set of forward rates (also called forward LIBORs), which have the advantage of being directly observable in the market, and whose volatilities are naturally linked to traded contracts. Each forward rate is modeled by a lognormal process under its forward measure, i.e. a Black model leading to a Black formula for interest rate caps. This formula is the market standard to quote cap prices in terms of implied volatilities, hence the term "market model". The LIBOR market model may be interpreted as a collection of forward LIBOR dynamics for different forward rates with spanning tenors and maturities, each forward rate being consistent with a Black interest rate caplet formula for its canonical maturity. One can write the different rates dynamics under a common pricing measure, for example the forward measure for a preferred single maturity, and in this case forward rates will not be lognormal under the unique measure in general, leading to the need for numerical methods such as monte carlo simulation or approximations like the frozen drift assumption. == Model dynamic == The LIBOR market model models a set of $n$ forward rates $L\_$, $j=1,\backslash ldots,n$ as lognormal processes. Under the respective $T\_j$ -Forward measure $Q\_\}\}(t)\backslash text$ Here, $L\_$ denotes the forward rate for the period $()$. For each single forward rate the model corresponds to the Black model. The novelty is that, in contrast to the Black model, the LIBOR market model describes the dynamic of a whole family of forward rates under a common measure. The question now is how to switch between the different $T$-Forward measures. By means of the multivariate Girsanov's theorem one can show〔(D. Papaioannou (2011): "Applied Multidimensional Girsanov Theorem", SSRN )〕〔("An accompaniment to a course on interest rate modeling: with discussion of Black-76, Vasicek and HJM models and a gentle introduction to the multivariate LIBOR Market Model" )〕 that :$$ dW^ dW^^ \frac _k(t) dt \qquad j < p \\ dW^}(t) + \sum\limits_^ \frac _k(t) dt \qquad \quad j > p \\ \end and :$$ dL_j(t) = \begin L_j(t)_j(t)dW^(t) - L_j(t)\sum\limits_^ \frac _j(t)_k(t)_dt \qquad j L_j(t)_j(t)dW^(t) \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \quad \quad j = p \\ L_j(t)_j(t)dW^(t) + L_j(t)\sum\limits_^ \frac _j(t)_k(t)_dt \quad \qquad j > p\\ \end 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「LIBOR market 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.