Construction and Application of Mixed Copula Model
Xueyan Pan*, Guanghui Cai**, and Qiulin Chen**
*School of Economics and Mangement, Anhui Normal Universtity
No. 189 Jiuhua South Road, Wuhu, Anhui 241002, China
**School of Statistics and Mathematics, Zhejiang Gongshang University
No.18 Xuezheng Street, Xiasha University Town, Hangzhou 310018, China
The Copula theory has been widely used in many scientific fields. In this study, we discuss model selection for the Copula theory. We derive the mixed Copula model based on the Kendall rank correlation coefficient. This new method is applied to forecast the value at risk of the portfolio in the foreign exchange market. The results show that the proposed mixed Copula model proposed in this paper is better than the other, commonly used, Copula model.
-  R. B. Nelson, “An Introduction to Copulas,” Springer, 2006.
-  P. Embrechts, A. McNeil, and D. Straumann, “Correlation: pitfalls and alternative,” Risk, Vol.12, No.5, pp. 69-71, 1999.
-  A. L. Valdés, L. A. Fraire, and R. D. Vázquez, “A copula-TGARCH approach of conditional dependence between oil price and stock market index: the case of Mexico,” Estudios Económicos, Vol.31, No.1, pp. 47-63, 2016.
-  G. Cheng, P. Li, and P. Shi, “A new algorithm based on copulas for VaR valuation with empirical calculations,” Theoretical Computer Science, Vol.378, pp. 190-197, 2007.
-  Z. Ouyang, H. Liao, and X. Yang, “Modeling dependence based on mixture copulas and its application in risk management,” Applied Mathematics – A J. of Chinese Universities, Vol.24, No.4, pp. 393-401, 2009.
-  Z. Cai and X. Wang, “Selection of mixed Copula model via penalized likelihood,” J. of the American Statistical Association, Vol.109, pp. 778-801, 2014.
-  N. Gregor and S. Marcus, “Mixture pair copula construction,” J. of Banking & Finance, Vol.54, pp. 175-191, 2015.
-  M. Longla, “On mixtures of copulas and mixing coefficients,” J. of Multivariate Analysis, Vol.139, pp. 259-265, 2015.
-  R. Mesiar, M. Komorníková, and J. Komorník, “Perturbation of bivariate copulas,” Fuzzy Sets and Systems, Vol.268, pp. 127-140, 2015.
-  S. Taylor, “Modeling Financial Time Series,” Wiley, 1986.