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題名 傅利葉轉換於亞式選擇權評價上之應用性研究
作者 蘇宥運
貢獻者 廖四郎<br>江彌修
<br>
蘇宥運
關鍵詞 傅利葉轉換
亞洲選擇權
快速傅利葉轉換
傅利業級數
日期 2004
上傳時間 14-Sep-2009 09:25:51 (UTC+8)
摘要 本論文介紹傅利葉轉換於亞式選擇權評價上的應用探討,並藉由與其他評價方式比較,來凸顯此評價方法不須對標的價格做分配假設的評價優勢,以及藉由快速傅利葉所具有的快速演算優勢,來看對亞式選擇權評價的影響。
參考文獻 中文部份
1. 陳松男,金融工程學:金融商品創新選擇權理論,華泰書局,民國91年。
英文部份
1. Alziary B., J. Decamps, and P. Koehl(1997), “A P.D.E. Approach to Asian Options:Analytical and Numerical Evidence,” Journal of Banking and Finance, 21, pp613-640.
2. Bakshi, G. and D. B. Madan(2000), “Spanning and Derivative Security Valuation,” Journal of Financial Economics, pp205-238.
3. Benhamou, E.(2002), “Fast Fourier Transform for Discrete Asian Options,” Journal of Computational Finance, 6.
4. Boyle, P.(1997), “Options :A Monte Carlo Approach,” Journal of Financial Economics, 4, pp323-338.
5. Carr P., and D. B. Madan(1999), “Option Valuation Using the Fast Fourier Transform,” Journal of Computational Finance, 2, pp61-73.
6. Caverhill A. and Clewlow L(1992), Flexible Convolution, From Black Scholes to Black Holes, pp165-171.
7. Corwin J., P. Boyle, and K. Tan(1996), “Quasi-Monte Carlo Methods in Numerical Finance,” Management Science, 42, pp926-938.
8. Dempster M., and S. Hong(2000), “Pricing Spread Option with the Fast Fourier Transform,” University of Cambridge working paper.
9. Dewynne J., and P. Wilmott(1995), “Asian Options as Linear Complementary Problems,” Advances in Futures and Options Research, 8, pp145-173.
10. Hewitt E., and K. R. Stromberg(1965), Real and Abstract Analysis, Springer-Verlag, New York.
11. Hull J., and A. White(1993), “Efficient Procedures for Valuing European and American Path Dependent Options,” Journal of Derivatives , 1, pp21-23.
12. Kemna A., and A. Vorst(1990), “A Pricing Method for Option Based on Average Asset Values,” Journal of Banking and Finance, 14, pp113-129.
13. Levy, E.(1992), ”Pricing European Average Rate Currency Options,” Journal of International Money and Finance, 11, pp474-491.
14. Levy E., and S. Turnbull(1992), “Beyond Average Intelligence,” RISK, 5 , pp53-59.
15. Madan, D. B., P. Carr, and E. Chang(1998), “The Variance Gamma Process and Option Pricing,” European Finance Review, 2, pp79-105.
16. Milevsky M. A., and S. E. Posner(1998), “Asian Options, the Sum of Lognormals, and the Reciprocal Gamma Distribution,” Journal of Financial and Quantitative Analysis , 33, pp409-422.
17. Milevsky M. A., and S. E. Posner(1999), “Another Moment for the Average Option,” Derivatives Quarterly, pp47-53.
18. Neave E., and S. Turnbull(1993), “Quick Solutions for Arithmetic Average Options on a Recombining Random Walk,” 4th Actuarial Approach for Financial Risks International Colloquium, pp718-739.
19. Turnbull S., and L. Wakeman(1991), “A Quick Algorithm for Pricing European Average Options,” Journal of Financial and Quantitative Analysis, 26, pp377-389.
20. Vorst T.(1992), “Prices and Hedge Ratios of Average Exchange Rate Options,” International Review of Financial Analysis, 1, pp179-193.
21. Roussas G.(1997), A Course in Mathematical Statistics, Academic Press.
22. Shephard N. G.(1991), “From Characteristic Function To Distribution Function:A Simple Framework For The Theory,” Econometric Theory, 7, pp519-529.
描述 碩士
國立政治大學
金融研究所
90352027
93
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0090352027
資料類型 thesis
dc.contributor.advisor 廖四郎<br>江彌修zh_TW
dc.contributor.advisor <br>en_US
dc.contributor.author (Authors) 蘇宥運zh_TW
dc.creator (作者) 蘇宥運zh_TW
dc.date (日期) 2004en_US
dc.date.accessioned 14-Sep-2009 09:25:51 (UTC+8)-
dc.date.available 14-Sep-2009 09:25:51 (UTC+8)-
dc.date.issued (上傳時間) 14-Sep-2009 09:25:51 (UTC+8)-
dc.identifier (Other Identifiers) G0090352027en_US
dc.identifier.uri (URI) https://nccur.lib.nccu.edu.tw/handle/140.119/31148-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 金融研究所zh_TW
dc.description (描述) 90352027zh_TW
dc.description (描述) 93zh_TW
dc.description.abstract (摘要) 本論文介紹傅利葉轉換於亞式選擇權評價上的應用探討,並藉由與其他評價方式比較,來凸顯此評價方法不須對標的價格做分配假設的評價優勢,以及藉由快速傅利葉所具有的快速演算優勢,來看對亞式選擇權評價的影響。zh_TW
dc.description.tableofcontents 第一章 緒論.......................1
     第二章 傅利葉級數、離散傅利葉轉換與快速傅利葉轉換....5
     第一節 傅利葉級數(Fourier Series). ... ......5
     第二節 離散傅利葉轉換(Discrete Fourier Transform). . 7
     第三節 快速傅利葉轉換(Fast Fourier Transform)......8
     第三章 快速傅利葉轉換應用至普通選擇權的評價.......11
     第一節 傳統傅利葉方法應用至選擇權的評價.........11
     第二節 選擇權價格的傅利葉轉換 ......... ....12
     第三節 價外選擇權價格(時間價值)的傅利葉轉換 . .....15
     第四節 運用快速傅利葉轉換至選擇權評價..........18
     第五節 各種評價方法精確性及有效性之比較.........19
     第四章 三種評價亞式選擇權的方法.............23
     第一節 以Levy(1992)評價亞式選擇權........... 23
     第二節 以Milevsky and Posner (1998)評價亞式選擇權. .24
     第三節 以Benhamou(2002)快速傅利葉轉換評價亞式選擇權...28
     第四節 近似封閉解評價公式準確度之比較..........34
     第五節 Caverhill and Clewlow(1992)、Benhamou (2002)
      與倒數Gamma 分配評價方法準確性之比較..... .35
     第五章 結論.................... .41
     參考文獻................... ..... 43
zh_TW
dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0090352027en_US
dc.subject (關鍵詞) 傅利葉轉換zh_TW
dc.subject (關鍵詞) 亞洲選擇權zh_TW
dc.subject (關鍵詞) 快速傅利葉轉換zh_TW
dc.subject (關鍵詞) 傅利業級數zh_TW
dc.title (題名) 傅利葉轉換於亞式選擇權評價上之應用性研究zh_TW
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) 中文部份zh_TW
dc.relation.reference (參考文獻) 1. 陳松男,金融工程學:金融商品創新選擇權理論,華泰書局,民國91年。zh_TW
dc.relation.reference (參考文獻) 英文部份zh_TW
dc.relation.reference (參考文獻) 1. Alziary B., J. Decamps, and P. Koehl(1997), “A P.D.E. Approach to Asian Options:Analytical and Numerical Evidence,” Journal of Banking and Finance, 21, pp613-640.zh_TW
dc.relation.reference (參考文獻) 2. Bakshi, G. and D. B. Madan(2000), “Spanning and Derivative Security Valuation,” Journal of Financial Economics, pp205-238.zh_TW
dc.relation.reference (參考文獻) 3. Benhamou, E.(2002), “Fast Fourier Transform for Discrete Asian Options,” Journal of Computational Finance, 6.zh_TW
dc.relation.reference (參考文獻) 4. Boyle, P.(1997), “Options :A Monte Carlo Approach,” Journal of Financial Economics, 4, pp323-338.zh_TW
dc.relation.reference (參考文獻) 5. Carr P., and D. B. Madan(1999), “Option Valuation Using the Fast Fourier Transform,” Journal of Computational Finance, 2, pp61-73.zh_TW
dc.relation.reference (參考文獻) 6. Caverhill A. and Clewlow L(1992), Flexible Convolution, From Black Scholes to Black Holes, pp165-171.zh_TW
dc.relation.reference (參考文獻) 7. Corwin J., P. Boyle, and K. Tan(1996), “Quasi-Monte Carlo Methods in Numerical Finance,” Management Science, 42, pp926-938.zh_TW
dc.relation.reference (參考文獻) 8. Dempster M., and S. Hong(2000), “Pricing Spread Option with the Fast Fourier Transform,” University of Cambridge working paper.zh_TW
dc.relation.reference (參考文獻) 9. Dewynne J., and P. Wilmott(1995), “Asian Options as Linear Complementary Problems,” Advances in Futures and Options Research, 8, pp145-173.zh_TW
dc.relation.reference (參考文獻) 10. Hewitt E., and K. R. Stromberg(1965), Real and Abstract Analysis, Springer-Verlag, New York.zh_TW
dc.relation.reference (參考文獻) 11. Hull J., and A. White(1993), “Efficient Procedures for Valuing European and American Path Dependent Options,” Journal of Derivatives , 1, pp21-23.zh_TW
dc.relation.reference (參考文獻) 12. Kemna A., and A. Vorst(1990), “A Pricing Method for Option Based on Average Asset Values,” Journal of Banking and Finance, 14, pp113-129.zh_TW
dc.relation.reference (參考文獻) 13. Levy, E.(1992), ”Pricing European Average Rate Currency Options,” Journal of International Money and Finance, 11, pp474-491.zh_TW
dc.relation.reference (參考文獻) 14. Levy E., and S. Turnbull(1992), “Beyond Average Intelligence,” RISK, 5 , pp53-59.zh_TW
dc.relation.reference (參考文獻) 15. Madan, D. B., P. Carr, and E. Chang(1998), “The Variance Gamma Process and Option Pricing,” European Finance Review, 2, pp79-105.zh_TW
dc.relation.reference (參考文獻) 16. Milevsky M. A., and S. E. Posner(1998), “Asian Options, the Sum of Lognormals, and the Reciprocal Gamma Distribution,” Journal of Financial and Quantitative Analysis , 33, pp409-422.zh_TW
dc.relation.reference (參考文獻) 17. Milevsky M. A., and S. E. Posner(1999), “Another Moment for the Average Option,” Derivatives Quarterly, pp47-53.zh_TW
dc.relation.reference (參考文獻) 18. Neave E., and S. Turnbull(1993), “Quick Solutions for Arithmetic Average Options on a Recombining Random Walk,” 4th Actuarial Approach for Financial Risks International Colloquium, pp718-739.zh_TW
dc.relation.reference (參考文獻) 19. Turnbull S., and L. Wakeman(1991), “A Quick Algorithm for Pricing European Average Options,” Journal of Financial and Quantitative Analysis, 26, pp377-389.zh_TW
dc.relation.reference (參考文獻) 20. Vorst T.(1992), “Prices and Hedge Ratios of Average Exchange Rate Options,” International Review of Financial Analysis, 1, pp179-193.zh_TW
dc.relation.reference (參考文獻) 21. Roussas G.(1997), A Course in Mathematical Statistics, Academic Press.zh_TW
dc.relation.reference (參考文獻) 22. Shephard N. G.(1991), “From Characteristic Function To Distribution Function:A Simple Framework For The Theory,” Econometric Theory, 7, pp519-529.zh_TW