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A General Computation Scheme for a High-Order Asymptotic Expansion Method
http://hdl.handle.net/2261/43065
http://hdl.handle.net/2261/43065317aa03e-02f7-47bd-a31b-2db93c06c942
Item type | テクニカルレポート / Technical Report(1) | |||||
---|---|---|---|---|---|---|
公開日 | 2017-01-17 | |||||
タイトル | ||||||
タイトル | A General Computation Scheme for a High-Order Asymptotic Expansion Method | |||||
言語 | ||||||
言語 | eng | |||||
キーワード | ||||||
主題 | Asymptotic Expansion | |||||
主題Scheme | Other | |||||
キーワード | ||||||
主題 | Malliavin Calculus | |||||
主題Scheme | Other | |||||
キーワード | ||||||
主題 | Approximation Formula | |||||
主題Scheme | Other | |||||
キーワード | ||||||
主題 | Stochastic Volatility | |||||
主題Scheme | Other | |||||
キーワード | ||||||
主題 | λ-SABR Model | |||||
主題Scheme | Other | |||||
キーワード | ||||||
主題 | Libor Market Model | |||||
主題Scheme | Other | |||||
キーワード | ||||||
主題 | Currency Options | |||||
主題Scheme | Other | |||||
資源タイプ | ||||||
資源 | http://purl.org/coar/resource_type/c_18gh | |||||
タイプ | technical report | |||||
アクセス権 | ||||||
アクセス権 | metadata only access | |||||
アクセス権URI | http://purl.org/coar/access_right/c_14cb | |||||
著者 |
Takahashi, Akihiko
× Takahashi, Akihiko× Takehara, Kohta× Toda, Masashi |
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著者所属 | ||||||
著者所属 | Graduate School of Economics, the University of Tokyo | |||||
抄録 | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | This paper presents a new computational scheme for an asymptotic expansion method of an arbitrary order. An asymptotic expansion method in finance initiated by Kunitomo and Takahashi[9], Yoshida[34] and Takahashi [20], [21] is a widely applicable methodology for an analytic approximation of the expectation of a certain functional of diffusion processes and not only academic researchers but also many practitioners have used the methodology for a variety of financial issues such as pricing or hedging complex derivatives under highdimensional underlying stochastic environments. In practical applications of the expansion, the crucial step is calculation of conditional expectations for a certain kind of Wiener functionals. [20], [21] and Takahashi and Takehara [23] provided explicit formulas of conditional expectations necessary for the asymptotic expansion up to the third order. <改行>This paper presents the new method for computing an arbitrary-order expansion in a general diffusion-type stochastic environment, which is powerful especially for a high-order expansion: This develops a new calculation algorithm for computing coefficients of the expansion through solving a system of ordinary differential equations that is equivalent to computing the conditional expectations. To demonstrate its effectiveness, the paper gives numerical examples of the approximation for the λ-SABR model up to the fifth order and a cross-currency Libor market model with a general stochastic volatility model of the spot foreign exchange rate up to the fourth order | |||||
内容記述 | ||||||
内容記述タイプ | Other | |||||
内容記述 | Revised version of CIRJE-F-621 (2009); subsequently published in International Journal of Theoretical and Applied Finance Vol. 15, No. 6 (2012). | |||||
内容記述 | ||||||
内容記述タイプ | Other | |||||
内容記述 | 本文フィルはリンク先を参照のこと | |||||
書誌情報 |
Discussion paper series. CIRJE-F 巻 CIRJE-F-787, 発行日 2011-02 |
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書誌レコードID | ||||||
収録物識別子タイプ | NCID | |||||
収録物識別子 | AA11450569 | |||||
フォーマット | ||||||
内容記述タイプ | Other | |||||
内容記述 | application/pdf | |||||
日本十進分類法 | ||||||
主題 | 335 | |||||
主題Scheme | NDC | |||||
出版者 | ||||||
出版者 | 日本経済国際共同センター | |||||
出版者別名 | ||||||
Center for International Research on the Japanese Economy | ||||||
関係URI | ||||||
識別子タイプ | URI | |||||
関連識別子 | http://www.cirje.e.u-tokyo.ac.jp/research/dp/2011/2011cf787ab.html | |||||
置換する | ||||||
関連タイプ | replaces | |||||
識別子タイプ | URI | |||||
関連識別子 | http://hdl.handle.net/2261/25747 |