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New Unified Computational Algorithm in a High-Order Asymptotic Expansion Scheme
http://hdl.handle.net/2261/35810
http://hdl.handle.net/2261/35810b43b17d9-08e4-4305-9770-2d6d593e81fc
Item type | テクニカルレポート / Technical Report(1) | |||||
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公開日 | 2017-01-17 | |||||
タイトル | ||||||
タイトル | New Unified Computational Algorithm in a High-Order Asymptotic Expansion Scheme | |||||
言語 | ||||||
言語 | eng | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | Asymptotic Expansion | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | Malliavin Calculus | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | Approximation Formula | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | Stochastic Volatility | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | λ-SABR Model | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | Libor Market Model | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | Currency Options | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | AMS Subject Classifications: 91G80, 91G20, 60H07, 60H30, 60H35 | |||||
資源タイプ | ||||||
資源タイプ識別子 | http://purl.org/coar/resource_type/c_18gh | |||||
資源タイプ | 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 |
Takehara, Kohta
× Takehara, Kohta× Takahashi, Akihiko× Toda, Masashi |
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著者所属 | ||||||
値 | Graduate School of Economics, the 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 [6] and Yoshida [29] is a widely applicable methodology for analytic approximation of the expectation of a certain functional of diffusion processes. Mathematically, this methodology is justified by Watanabe theory([27]) in Malliavin calculus.// In practical applications, it is desirable to investigate the accuracy and stability of the method especially with expansion up to high orders in situations where the underlying processes are highly volatile as seen in the recent financial markets.// Although Takahashi[17], [18] and Takahashi and Takehara [20] provided explicit formulas for the expansion up to the third order, to our best knowledge a general computation scheme for an arbitraryorder expansion has not been given yet.// This paper proposes two general methods for computing the conditional expectations that are powerful especially for high order expansions: The first one, as an extension of the method introduced by the preceding papers, presents a unified scheme for computation of the conditional expectations. 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 - 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 | Subsequenlty published in The Proceedings of KIER-TMU International Workshop on Financial Engineering, pp. 231-251, 2010, World Scientifc, June, 2011. | |||||
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-728, 発行日 2010-03 |
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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Scheme | NDC | |||||
主題 | 335 | |||||
出版者 | ||||||
出版者 | 日本経済国際共同センター | |||||
出版者別名 | ||||||
値 | 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/2010/2010cf728ab.html |