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Computation in an Asymptotic Expansion Method
http://hdl.handle.net/2261/25747
http://hdl.handle.net/2261/2574752d16a3e-82fb-4d9e-9281-014ca3e801ea
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 | Computation in an Asymptotic Expansion Method | |||||
言語 | ||||||
言語 | eng | |||||
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× Kohta, Takehara× Masashi, Toda |
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著者所属 | ||||||
著者所属 | University of Tokyo | |||||
抄録 | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | An asymptotic expansion scheme in finance initiated by Kunitomo and Takahashi [15] and Yoshida[68] is a widely applicable methodology for analytic approximation of the expectation of a certain functional of diffusion processes. [46], [47] and [53] provide explicit formulas of conditional expectations necessary for the asymptotic expansion up to the third order. In general, the crucial step in practical applications of the expansion is calculation of conditional expectations for a certain kind of Wiener functionals. This paper presents two methods for computing the conditional expectations that are powerful especially for high order expansions: The first one, an extension of the method introduced by the preceding papers presents a general scheme for computation of the conditional expectations and show the formulas useful for expansions up to the fourth order explicitly. The second one develops a new calculation algorithm for computing the coefficients of the expansion through solving a system of ordinary differential equations that is equivalent to computing the conditional expectations. To demonstrate their effectiveness, the paper gives numerical examples of the approximation for 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 | forthcoming in International Journal of Theoretical and Applied Finance (as CIRJE-F-787). | |||||
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-621, 発行日 2009-05 |
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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/2009/2009cf621ab.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/2261/43065 |