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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/37746完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 彭?堅 | |
| dc.contributor.author | You-Chen Chang | en |
| dc.contributor.author | 張祐誠 | zh_TW |
| dc.date.accessioned | 2021-06-13T15:41:40Z | - |
| dc.date.available | 2008-07-27 | |
| dc.date.copyright | 2008-07-27 | |
| dc.date.issued | 2008 | |
| dc.date.submitted | 2008-07-07 | |
| dc.identifier.citation | [1] K. Amin. Jump diffusion option valuation in discrete time. J. Finance,
48:1833–1863, 1993. [2] U. Ascher, S. Ruuth, and R. J. Spiteri. Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations. Appl. Numer. Math., 25:151–167, 1997. [3] A. Bensoussan and J.-L. Lions. Impulse Control and Quasi-Variational Inequalities. Gauthier-Villars, Paris, 1984. [4] M. Briani, C. La Chioma, and R. Natalini. Convergence of numer- ical schemes for viscosity solutions to integro-differential degenerate parabolic problems arising in financial theory. Numer. Math., 98:607– 646, 2004. [5] M. Briani, R. Natalini, and G. Russo. Implicit-explicit numerical schemes for jump-diffusion processes. Calcolo., 44:33–57, 2007. [6] E. Oran Brigham. The Fast Fourier Transform and Its Applications. Prentice-Hall, Inc., 1988. [7] J. C. Butcher. Numerical Methods for Ordinary Differential Equations. John Wiley & Sons, 2003. [8] R. Cont and P. Tankov. Financial Modelling with Jump Processes. Chap-man & Hall/CRC, 2004. [9] C. M. Elliott and J. R. Ockendon. Weak and Variational Methods for Moving Boundary Problems. Pitman, Boston, 1982. [10] P. A. Forsyth and K. R. Vetzal. Quadratic convergence of a penalty method for valuing American options. SIAM J. Sci. Comput., 23:2096– 2123, 2002. [11] E. Hairer and G. Wanner. Solving Ordinary Differential Equations, Vol.2. Springer-Verlag, New York, 1991. [12] Y. Halluin, P. A. Forsyth, and G. Labahn. A penalty method for American options with jump diffusion processes. Numer. Math., 97:321– 352, 2004. [13] R. Merton. Option pricing when underlying stock returns are discontin-uous. J. Financial Economics, 3:125–144, 1976. [14] L. Pareschi and G. Russo. Implicit-explicit Runge-Kutta schemes for stiff systems of differential equations. Adv. Theory Comput. Math., 3:269– 289, 2001. [15] L. Pareschi and G. Russo. Implicit-explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxation. SIAM J. Sci. Com-put., 25:129–155, 2005. [16] W.H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery. Numerical Recipes in C: the Art of Scientific Computing. Cambridge University Press: Cambridge, 1992. [17] K.-I. Sato. L´evy Processes and Infinitely Divisible Distributions. Cam-bridge University Press, 1999. [18] James S. Walker. Fast Fourier Transforms. CRC Press, Inc., 1991. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/37746 | - |
| dc.description.abstract | 本篇論文主要是探討如何利用 IMEX 的方法為跳躍市場的選擇權定價。除了一階的方法之外，我們還會探討多階的 Runge-Kutta 方法。最後我們還會以數值的結果來探討利用 Runge-Kutta 方法的優勢所在。 | zh_TW |
| dc.description.abstract | This paper mainly discusses how to use the IMEX method to price options on a market with jumps. In addition to the first order method, we will discuss the IMEX Runge-Kutta method which is a higher order scheme. Finally, we will use the numerical examples to discuss the advantage of the IMEX Runge-Kutta method. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-13T15:41:40Z (GMT). No. of bitstreams: 1 ntu-97-R94221033-1.pdf: 298904 bytes, checksum: 1962b9e9580bcddc0c7aef1e2f1bcc76 (MD5) Previous issue date: 2008 | en |
| dc.description.tableofcontents | 中文摘要 . . i
英文摘要 . . i 第一章 Introduction . . 1 第二章 Jump diffusion model and European option . . 2 2.1 Some background knowledge . . 2 2.2 PIDE for pricing European options in a market with jumps . . 4 2.3 IMEX on PIDE . . 6 2.4 FFT implementation . . 10 第三章 Jump diffusion model and American option: the first algorithm . . 12 第四章 Jump diffusion model and American option: IMEX Runge-Kutta scheme . . 17 第五章 Numerical comparison of the two algorithms . . 27 參考文獻 . . 31 | |
| dc.language.iso | en | |
| dc.subject | 朗格-古塔的方法 | zh_TW |
| dc.subject | 有限插分方法 | zh_TW |
| dc.subject | 含有跳躍的擴散過程 | zh_TW |
| dc.subject | 隱式-顯式的方法 | zh_TW |
| dc.subject | 無條件地穩定 | zh_TW |
| dc.subject | 快速傅立葉轉換 | zh_TW |
| dc.subject | Jump diffusion process | en |
| dc.subject | Unconditionally stable | en |
| dc.subject | IMEX method | en |
| dc.subject | Finite difference method | en |
| dc.subject | Runge-Kutta scheme | en |
| dc.subject | Fast Fourier transform | en |
| dc.title | 用在跳躍市場的隱式－顯式之定價方法 | zh_TW |
| dc.title | IMEX Method For A Market With Jumps | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 96-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 陳宜良,謝南瑞 | |
| dc.subject.keyword | 有限插分方法,含有跳躍的擴散過程,隱式-顯式的方法,無條件地穩定,快速傅立葉轉換,朗格-古塔的方法, | zh_TW |
| dc.subject.keyword | Finite difference method,Jump diffusion process,IMEX method,Unconditionally stable,Fast Fourier transform,Runge-Kutta scheme, | en |
| dc.relation.page | 32 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2008-07-07 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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