自從Black-Scholes發表其選擇權訂價理論後，對於選擇權的發展貢獻極大，更加速各種新奇選擇權的發展，其中之一就是彩虹選擇權，也就是選擇權的標的資產不僅一個股票，它可能包括兩個股票(two color rainbow option)、三個股票
(three color rainbow option)或甚至n個股票皆有可能，本研究在介紹兩個標的資產的彩虹選擇權的定價模型，比較雙變數GARCH以及Copula這兩個定價模型的差別。本研究以蒙地卡羅模擬法對標的資產進行股價模擬，而發現到以假設兩標的資間的相關性是常態分配或T分配時，其績效都比假設Copula來的差，而尤其又以動態調整的Copula來的最為理想。

After Black-Scholes advert to the option pricing theory, it has a great contribution to the advance of option；speed up all kinds of Exotic Options, one of it is Rainbow Options. Rainbow Options are their underlying assets which are not only one stock, but it may include two stocks or three stocks even more. Our studies  introduce the two color rainbow option of its pricing model, to compare the difference with Bivariate garch model and Copula model. Our study use Monte Carlo Simulation to simulate underlying assets. We discover that if we assume the relationship of two underlying to yield to normal distribution or T distribution it results are worse than Copula. Specifically dynamic Copula are the best.

目錄
第一章 緒論...............................................1
  第一節 研究動機與目的...................................1
  第二節 研究流程.........................................2
  第三節 研究架構.........................................3
第二章 文獻回顧和探討.....................................4
  第一節 彩虹選擇權評價模型的相關文獻探討.................4
  第二節 Copula在財務計量、風險管理以及選擇權定價上的應用.7
第三章 研究方法..........................................10
  第一節 Copula的基本定義定理介紹........................10
  第二節 選擇權定價的基本概念............................14
  第三節 標的股價預估與選擇權定價........................15
  第四節 波動性的估計....................................21
  第五節 以靜態Copula評價彩虹選擇權......................25
  第六節 以動態Copula評價彩虹選擇權......................31
第四章 實證分析..........................................33
  第一節 資料來源與變數定義..............................33
  第二節 參數估計、標的資產、選擇權價格模擬與績效評估結果34
第五章 結論與建議........................................51
附錄:二元彩虹選擇權價格的模擬結果........................52
參考文獻...............................................64  

【目 次】
【表3-1】Copula函數................................................................................................27
【表3-2】 Kendall’s tau...............................................................................................27
【表4-1】電子類股價指數與金融類股價指數........................................................34
【表4-2】電子類股價指數與大盤股價指數............................................................35
【表4-3】金融類股價指數與大盤股價指數............................................................36
【表4-4】電子及金融................................................................................................37
【表4-5】電子及大盤................................................................................................37
【表4-6】金融及大盤................................................................................................37
【表4-7】三個月後電子類股價指數與金融類股價指數........................................38
【表4-8】三個月後電子類股價指數與大盤股價指數............................................39
【表4-9】三個月後金融類股價指數與大盤股價指數............................................40
【表4-10】電子類股價指數與金融類股價指數......................................................49
【表4-11】電子類股價指數與大盤股價指數..........................................................49
【表4-12】金融類股價指數與大盤股價指數..........................................................50










【圖 次】
【圖1-1】架構流程圖...............................................................................................3
【圖4-1a】以電子類指數與金融類指數為標的資產的二元彩虹選權.................41
【圖4-1b】以電子類指數與金融類指數為標的資產的二元彩虹選權...............41
【圖4-1c】以電子類指數與金融類指數為標的資產的二元彩虹選權...............42
【圖4-1d】以電子類指數與金融類指數為標的資產的二元彩虹選權................42
【圖4-2a】以電子類指數與大盤類指數為標的資產的二元彩虹選權...............43
【圖4-2b】以電子類指數與大盤類指數為標的資產的二元彩虹選權...............43
【圖4-2c】以電子類指數與大盤類指數為標的資產的二元彩虹選權................44
【圖4-2d】以電子類指數與大盤類指數為標的資產的二元彩虹選權................44
【圖4-3a】以金融類指數與大盤類指數為標的資產的二元彩虹選權..............45
【圖4-3b】以金融類指數與大盤類指數為標的資產的二元彩虹選權................45
【圖4-3c】以金融類指數與大盤類指數為標的資產的二元彩虹選權................46
【圖4-3d】以金融類指數與大盤類指數為標的資產的二元彩虹選權................46

一、中文部分
1.	柯鈞逵(2000)，〝時間相依相關係數下多資產選權之評價〞，國立台灣大學
   財務融研究所碩士論文。
2.	朱家昌(2001)，〝GRACH過程下相關資產選擇權之定價〞，國立清華大學統計學研究所碩士論文。
3.	邱騰達(2004)，〝彩虹選擇權之相關係數風險探討〞，國立中正大學財務金
   融研究所碩士論文。
4.	李沃牆、黃淑菁(2005)，〝以蒙地卡羅模擬法評價彩虹選擇權〞，私立真理大學財務金融研究所。
5.	廖四郎、李福慶(2005)，〝擔保債權憑證之評價－Copula分析法〞，國立政治大學金融系。
6.	周宗南、劉瑞鑫(2003)，〝時間序列與人工智慧方法在台股指數報酬率預測之績效比較〞，私立朝陽科技大學財務金融系。



二、英文部分
1.	Acworth, P., M. Broadie, and P. Glasserman(1996),〝A comparison of some Monte Carlo and Quasi Monte Carlo techinques for option pricing〞
,Working paper.
2.	Black, F. and J. C. Cox (1976), 〝Valuing corporate securities: some effects of bond indenture provisions〞,Journal of Finance 31,pages351-367.
3.	Black, F. and Scholes, M.S.(1973), 〝The pricing of options and corporate liabilities 〞, J. Pol. Econ. 81, pages 637-654.
4.	Cherubini, U. and Luciano, E.(2002), 〝 Bivariate option pricing with copulas 〞, Appl. Math. Finan. 9, pages 69–86.
5.	Duffie, D. and K. Singleton (1999), 〝Modeling term structure of defaultable bonds〞, Review of Financial Studies, 12, pages 687-720.
6.	Duan, J.-C., 1995. 〝The GARCH option pricing model 〞 Math. Finan.5, pages 13-32
7.	Gibson M. S. and B. H. Boyer (1998), 〝Evaluating forecasts of correlation using option pricing〞, Board of Governors of the Federal Reserve System International Finance Discussion Paper, No.600.
8.	Hans N. and E. Bystrom (2001), 〝Using simulated currency rainbow options to evaluate covariance matrix forecasts〞, Department of Economics, Lund University, P.O. Box 7082, S-220 07 Lund, Sweden, Working paper.
9.	Johnson, H. (1987), 〝Options on the maximum or minimum of several assets〞, Journal of Financial and Quantitative Analysis, Vol.22,p.277-283
10.	Jarrow, R. and S. Turnbull (1995), 〝Pricing derivatives on financial securities subject to credit risk〞,Journal of Finance 50 , pages 53- 85.
11.	Lando, D. (1998), 〝On cox processes and credit risky securities〞,Review of Derivative Research, Vol.2, pages 99-120.
12.	Levy, G. (2002), 〝Multi-asset derivative pricing using quasi-random numbers and Monte Carlo simulation〞,  NAG paper.
13.	Margrabe, W. (1978), 〝The value of an option to exchange one asset to another〞, Journal of Finance, pages 117-186.
14.	Merton, R. (1974), 〝On the pricing of corporate debt: The risk structure of interest rates 〞, Journal of Finance 29, pages 449-470.
15.	Patton, A.J.(2003). 〝 Modeling asymmetric exchange rate dependence 〞,
        Discussion Paper 01–09, University of California, San Diego,CA.
16.	Goorbergh,R.W.J. , Genest,C. , Werker,B.J.M.(2005),〝 Bivariate option pricing using dynamic copula models〞, Mathematics and Economics37
pages 101-114  

17.	Rosenberg, J.V. (1999), 〝 Semiparametric pricing of multivariate contingent claims〞, Working Paper S-99–35, Stern School of Business,New York University, New York.
18.	Rosenberg, J.V.( 2003), 〝Nonparametric pricing of multivariate contingent claims〞, Journal of Derivatives 10, pages 9-26.
19.	Rubinstein, M., (1991),〝Somewhere Over the Rainbow〞, RISK4, pp.63-66.
20.	Rubinstein, M., (1994),〝Return to Oz〞, RISK7, pp.67-71.
21.	Stulz, R.M., (1982),〝Options on the Minimum or the Maximum of Two Risky Assets: Analysis and Applications〞,Journal of Financial Economics, pp.161-185.
22.	Topper, J. (2001), 〝Worst Case Pricing of Rainbow Options〞,Discussion Paper,Np.217.
23.	Umberto, C. ， Elisa, L. and Walter, V. (2004), 〝Copula Methods in Finance〞.
24.	Wu, H. C. (2004), 〝 Pricing European Options Based on the Fuzzy Pattern of Black-Scholes Formula〞, Computers and Operations Research, Vol.31, No.7, pp.1069-1081.
25.	Zhou, C. (2001), 〝An analysis of default correlations and multiple defaults〞,The Review of Financial Studies,Vol.14(2),pages 555-576.