請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/43026完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 呂育道(Yuh-Dauh Lyuu) | |
| dc.contributor.author | Yu-Cheng Tien | en |
| dc.contributor.author | 田宇正 | zh_TW |
| dc.date.accessioned | 2021-06-15T01:33:24Z | - |
| dc.date.available | 2011-07-28 | |
| dc.date.copyright | 2009-07-28 | |
| dc.date.issued | 2009 | |
| dc.date.submitted | 2009-07-19 | |
| dc.identifier.citation | [1] Barraquand, J., and T. Pudet: “Pricing of American Path-Dependent Contingent Claims”, Math. Finance, 6, 17–51, 1996.
[2] Benhamou, E.: “Fast Fourier Transform for Discrete Asian Options.” Journal of Computational Finance, 6, 46–61, 2002. [3] Black, Fischer, and Myron Scholes: “The Pricing of Options and Corporate Liabilities”, Journal of Political Economy, 81, 637–654, 1973. [4] Boyle, P. P., M. Broadie, and P. Glasserman: “Monte Carlo Methods for Security Pricing”, Journal of Economic Dynamics and Control, 21, 1267–1321, 1997. [5] Broadie, M., and P. Glasserman: “Estimating Security Price Derivatives using Simulation”, Management Science, 42, 269–285, 1996. [6] Carverhill, Andrew, and Les Clewlow: “Flexible Convolution”, Risk, 5, 25–29, 1990. [7] Chesney, M. and L. Scott: “Pricing European Currency Options: a Comparison of the Modified Black-Scholes Model and a Random Variance Model”, Journal of Financial and Quantitative Analysis, 24, 267–284, 1989. [8] Chiu, Chun-Yuan: “Efficient Pricing of Asian Options via the Fast Fourier Transform”, Master’s Thesis, Department of Computer Science & Information Engineering, National Taiwan University, Taipei, Taiwan, 2008. [9] Dai, T.-S., and Y.-D. Lyuu: “An Efficient Convergent Lattice Algorithm for European Asian Options”, Acta Informatica, 44, 23–39, 2007. [10] Isaacson, E., and H. B. Keller: Analysis of Numerical Methods, Wiley, New York, 1996. [11] Harrison, J.M., and S.R. Pliska: “Martingales and Stochastic Integrals in the Theory of Continuous Trading”, Stochastic Process, Appl. 11, 215–260, 1981. [12] Henderson, V., and R. Wojakowski: “On the Equivalence of Floating and Fixed-Strike Asian Options”, Journal of Applied Probability, 39, 391–394, 2002 [13] Hsu, William Wei-Yuan and Yuh-Dauh Lyuu: “A Convergent Quadratic-Time Lattice Algorithm for Pricing European-Style Asian Options”, Applied Mathematics and Computation, 189, 1099-1123, 2007. [14] Hull, J and A. White: “The Pricing of Options on Assets with Stochastic Volatilities”, The Journal of Finance 17, 281–300, 1987. [15] Hocking, J.R.M., G. Bonti, and D. Siegel: “Beyond the Lognormal”, Risk, 13(5), 59–62, 2000. [16] Huisman, R., K. G. Koedijk, and R. A. J. Pownall: “VaR-x: Fat Tails in Financial Risk Management”. Journal of Risk, 1(1), 47–61, 1998. [17] Kemna, A. G. Z., and A. C. F. Vorst: “A Pricing Method based on Average Asset Values”, Journal of Banking and Finance, 14, 113–129, 1990. [18] King, J. Thomas: Introduction to Numerical Computation, McGraw-Hill, New York, 166–174, 1984. [19] Levy, E.: “Pricing European Average Rate Currency Options”, Journal of International Money and Finance, 11, 474–491, 1992. [20] Milevsky, M. A., and S. E. Posner: “Asian Options, the Sum of Lognormals, and the Reciprocal Gamma Distribution”, Journal of Financial and Quantitative Analysis, 33, 409–422, 1998. [21] Ritchken, P., L. Sankarasubramanian, and A. M. Vijh: “The valuation of Path Dependent Contracts on the Average”, Management Science, 39, 1202-1213, 1993. [22] Turbull, S.M., and L.M. Wakeman: “A Quick Algorithm for Pricing European Average Options”, Financial and Quantitative Analysis, 26, 377–389, 1991. [23] Zhang, P. G.: Exotic Options: A Guide to Second Generation Options, World Scientific, Singapore, 1998. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/43026 | - |
| dc.description.abstract | 本文將指出一種有效率性的演算法，可以快速而準確地求算離散式固定履約價型亞式選擇權價格。這個演算法並不依賴Black-Scholes假設，在應用上具有彈性，可以適用於多種對於標的價格分配的假設以符合實證現象，例如：厚尾現象。
本文將延伸Carverhill-Clewlow (1990)和Benhamou (2002)的結果，在快速傅利葉轉換之上加入Simpson法則和三次多項式內插法以提升計算精確度。 | zh_TW |
| dc.description.abstract | In this thesis, we introduce an efficient algorithm for pricing discrete Asian options with fixed strike price. Our algorithm does not rely on the Black-Scholes assumption and is flexible for many kinds of underlying densities. Our algorithm can be applied to capturing many empirical phenomena, such as fat-tail effect.
Based on the Fast Fourier Transform (FFT), our algorithm using Simpson’s rule and the 3rd-order polynomial interpolation is an enhanced version of the algorithms of Carverhill and Clewlow (1992) and Benhamou (2002). The contribution of this thesis is an improved convergence rate to the order of 4. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-15T01:33:24Z (GMT). No. of bitstreams: 1 ntu-98-R96723025-1.pdf: 538946 bytes, checksum: f70650deda7743d999b2334018233cb8 (MD5) Previous issue date: 2009 | en |
| dc.description.tableofcontents | 口試委員會審定書 i
誌謝 ii 摘要 iii Abstract iv 目 錄 v 第一章 緒論 1 第一節 文獻回顧 1 第二節 研究目的 2 第三節 章節大綱 2 第二章 模型基礎 4 第一節 定義與假設 4 第二節 遞迴表示式與褶積：Carverhill-Clewlow演算法 5 第三節 重中央化：Benhamou演算法 7 第四節 數值積分公式：Simpson法則 8 第三章 四階收歛演算法 10 第一節 應用快速傅利葉轉換於Simpson法則 10 第二節 三次多項式內插法 13 第四章 數值結果 15 第一節 誤差收歛速率 15 第二節 時間複雜度 17 第三節 重中心化之效果 18 第五章 結論 19 參考文獻 20 | |
| dc.language.iso | zh-TW | |
| dc.subject | 多項式內插法 | zh_TW |
| dc.subject | 亞式選擇權 | zh_TW |
| dc.subject | 快速傅利葉轉換 | zh_TW |
| dc.subject | 褶積 | zh_TW |
| dc.subject | 辛普森法則 | zh_TW |
| dc.subject | convolution | en |
| dc.subject | polynomial interpolation | en |
| dc.subject | Asian Option | en |
| dc.subject | Fast Fourier Transformation | en |
| dc.subject | FFT | en |
| dc.title | 亞式選擇權評價：使用快速傅利葉轉換與辛普森法則 | zh_TW |
| dc.title | Asian Option Pricing with the Fast Fourier Trasformation and Simpson's Rule | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 97-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 戴天時(Tian-Shyr Dai),金國興 | |
| dc.subject.keyword | 亞式選擇權,快速傅利葉轉換,褶積,辛普森法則,多項式內插法, | zh_TW |
| dc.subject.keyword | Asian Option,Fast Fourier Transformation,FFT,convolution,polynomial interpolation, | en |
| dc.relation.page | 22 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2009-07-20 | |
| dc.contributor.author-college | 管理學院 | zh_TW |
| dc.contributor.author-dept | 財務金融學研究所 | zh_TW |
| 顯示於系所單位： | 財務金融學系 | |
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