セミナー発足に際してのごあいさつ(1997.4)


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第 204 回 Q-NA セミナー~
第 205 回 Q-NA セミナー~
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日時  : 2007 年 6月 12日(火曜) 15:30 - 17:00~
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場所  : 九州大学箱崎キャンパス 理学部 3号館 3階 3311 号室~
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演者  : [[Cornelis W. Oosterlee>http://ta.twi.tudelft.nl/users/oosterlee/]]~
     (Delft Institute of Applied Mathematics, Delft University of Technology, ~
     and CWI--Center for Mathematics and Computer Science)~
講演者 : [[Cornelis W. Oosterlee>http://ta.twi.tudelft.nl/users/oosterlee/]]~
     (Delft Institute of Applied Mathematics, ~
     Delft University of Technology, ~
     and CWI--Center for Mathematics and Computer Science,~
     Amsterdam, the Netherlands)~
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共著者 : R. Lord (Rabobank International), F. Fang (Delft University of Technology),~
     F. Bervoets (Rabobank International)~
共著者 : R. Lord (Rabobank International), ~
     F. Fang (Delft University of Technology),~
     F. Bervoets (Rabobank International)~
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題目  : A Fast and Accurate FFT-Based Method for Pricing Early-Exercise Options under L'evy Processes~
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講演概要: ~
When valuing and risk-managing exotic derivatives, practitioners demand fast and accurate prices and sensitivities.  Aside from non-standard exotic derivatives, plain vanilla options in many stock markets are actually of the American type. As any pricing and risk management system has to be able to calibrate to these plain vanilla options, it is import to value these American options quickly and accurately.
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A fast and accurate method for pricing early exercise and certain exotic options in computational finance is presented. The method is based on a quadrature technique and relies heavily on Fourier
transformations.  The main idea is to reformulate the well-known risk-neutral valuation formula by recognizing that it is a convolution. The resulting convolution is dealt with numerically by using the Fast Fourier Transform (FFT).
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The only requirement of the method is that the conditional characteristic function of the underlying asset is known, which is the case for many exponential L'evy models. In contrast to the solution methods based partial integro-differential operators, processes of infinite activity, such as the Variance Gamma (VG) or CGMY models can be handled with relative ease. In addition to its flexibility, a real benefit of our method is its impressive computational speed, as all integrations can be evaluated using the FFT algorithm. Its high accuracy and speed are demonstrated by pricing several Bermudan and American options under Geometric Brownian Motion (GBM), VG and CGMY.


世話人
田上 大助 (九州大学 マス・フォア・インダストリ研究所)
渡部 善隆 (九州大学 情報基盤研究開発センター)

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