臺灣博碩士論文加值系統

評價多資產衍生性標的，在理論推導和計算上相當複雜，尤其當投資組合標的資產個數很大時，幾乎無法準確找出聯合機率分配。直到copula 方法的提出，我們方可簡化處理上述的問題，配適出更符合實際的聯合機率分配。
本篇研究分別採用了skew t copula 及 t copula 關聯結構搭配指數加權平均法估計相關性進而估計某一商品期貨投資組合的風險值。我們發現兩模型皆通過了回朔測試並且也在壓力測試中，也快速地反映了左尾極端事件造成的影響。最後，我們針對此一期貨投資組合內各類別報酬率的相關性進行探討，發現相關性幾乎為正，尤其是在2008金融海嘯後此現象更加明顯。

1.Introduction……………………………………………………………..….....………...1
2.Literature Review………………………………………………….….....………………3
3.Data………………………………………………………………………………...............5
4.Methodology…………………………………………………………...……….....……...7
4.1 Basic concepts…………………………………………..……………….....…..…7
4.1.1 Copula function…………………………………...…………….....……….7
4.1.2 Sklar’s theorem……………………………………..……………......…..7
4.1.3 The multivariate skew t distribution…….......8
4.1.4 The multivariate t distribution………………........9
4.2 Calculating the VaR………………….…………………………………….....…9
4.3 The tests of backward testing and correlation….14
4.3.1Kupeic’s test…………………………………………….…………...........14
4.3.2Chrisofferson’s test…………………………………....….……………..15
4.3.3Spearman’s rank correlation and Hotelling Pabst’s test...............................................17
4.3.4 Kendall’s rank correlation test…………..….…………….18
5.Empirical result…………………………………………………………......…….……20
5.1 Backward testing……………………………………………........………………20
5.2 Stress testing…………………………………...……….…...…………………..25
5.3 Correlation…………………………………………….........……………………..29
6.Conclution………………………………………………..........………………………….35
Reference…………………………………………………...........…………………………..38
Appendix…………………………………………………............…………………………..40

1. Aas, K. and Haff, I.(2006), “The generalized hyperbolic skew student’s t distribution", Journal of financial econometrics 4, No.2: 275-309.
2.Berkowitz, J. and O’Brien, J. (2002)” How Accurate Are Value-at-Risk Models at Commercial Banks?”, The Journal of Finance, Vol.57, No.3.
3.Clemen, R. T. and Reilly, T(1997),”Correlations and copula for decision and risk analysis.”, Management Science, Vol.45, No.2, 208.
4.Culp, C., Miller, M. and Neves, A.(1998),” Value at risk: Uses and abuses”, Journal of Applied Corporate Finance, Vol. 10, Issue. 4, 26-38.
5.Demarta, S. and McNeil, A. J. (2004),”The t Copula and Related Copulas”, 2-10.
6.Hu, W. and A, Kercheval.(2007), “Risk management with generalized hyperbolic distributions”,Working paper,Florida State University, Tallahassee, USA.
7.J.P. Morgan.(1995), ”RiskMetrics”, Third Edition, J.P. Morgan.
8.Lin, J.L. and Liou, Z.K.(2009), “The dynamic t Copula with analytic estimation of degree of freedom in risk management of commodity futures
portfolio.”,Taiwan futures and derivative products journal,Vol.9,No.1, 1-35.
9.McNeil, A. J., Frey, P. and Embrechts, P.(2005),”Quantitative risk Management: Concepts,Techniques and Tools”,184-186.
10.Nieppola, O.(2009),”Backtesting Value-at-risk Models”,17-28.
11.Romano, C(2002), “Applying copula function to risk management.”,Working paper.
12.Yen, Y. Z.(2010),”Nonparametric Statistics”,NTU College of Management,325-332.
13.Yeh, H.C.(2009),”Advanced Statistics”, NTU College of Management, 231-234.