VaR Estimation of Multivariate Distribution Using Copula Functions

Title & Authors
VaR Estimation of Multivariate Distribution Using Copula Functions
Hong, Chong-Sun; Lee, Jae-Hyung;

Abstract
Most nancial preference methods for market risk management are to estimate VaR. In many real cases, it happens to obtain the VaRs of the univariate as well as multivariate distributions based on multivariate data. Copula functions are used to explore the dependence of non-normal random variables and generate the corresponding multivariate distribution functions in this work. We estimate Archimedian Copula functions including Clayton Copula, Gumbel Copula, Frank Copula that are tted to the multivariate earning rate distribution, and then obtain their VaRs. With these Copula functions, we estimate the VaRs of both a certain integrated industry and individual industries. The parameters of three kinds of Copula functions are estimated for an illustrated stock data of two Korean industries to obtain the VaR of the bivariate distribution and those of the corresponding univariate distributions. These VaRs are compared with those obtained from other methods to discuss the accuracy of the estimations.
Keywords
Condence level;dependence;earnings rate;generator;risk;
Language
Korean
Cited by
1.
다차원 Copula 함수를 이용한 VaR 추정,홍종선;이원용;

응용통계연구, 2011. vol.24. 5, pp.809-820
2.
Vector at Risk와 대안적인 VaR,홍종선;한수정;이기쁨;

응용통계연구, 2016. vol.29. 4, pp.689-697
1.
Vector at Risk and alternative Value at Risk, Korean Journal of Applied Statistics, 2016, 29, 4, 689
2.
VaR Estimation with Multiple Copula Functions, Korean Journal of Applied Statistics, 2011, 24, 5, 809
References
1.
김명직, 신성환 (2003). Copula 함수의 추정과 시뮬레이션, 선물연구, 11, 103-131.

2.
여성칠 (2006). 코퓰러와 극단치이론을 이용한 위험척도의 추정 및 성과분석, 응용통계연구, 19, 481-504.

3.
황수영 (2005). Copula 함수와 극단치 이론을 이용한 Value at Risk 측정에 관한 실증연구, 한국과학기술원, 박사학위논문.

4.
홍종선, 권태완 (2010). 수익률분포의 적합과 리스크값 추정, 한국데이터정보과학회지, 21, 219-229.

5.
Bae, K. H. and Karolyi, A. (2003). A new approach to measuring financial contagion, Review of Financial Studies, 16, 717-763.

6.
Breymann, W. (2003). Dependence structures for multivariate high-frequency data in finance, Quantitative Finance, 3, 1-14.

7.
Genest, C. and MacKay, J. (1986). The joy of copulas: Bivariate distributions with Uniform marginals, The American Statisticain, 40, 280-283.

8.
Jorion, P. (1997). Value at Risk, McGraw-Hill, New York.

9.
Li, D. X. (1999). Value at Risk based on the Volatility Skewness and Kurtosis, RiskMetrics Group.

10.
Longin, S. (2001). Extreme correlation of international equity markets, The Journal of Finance, 2, 649-676.

11.
Nelson, R. B. (2006). An Introduction to Copula, 6th Edition, Springer.

12.
Sklar, A. (1959). Fonctions de repartition a n dimensions et leurs marges, l'Institut de Statistique de L'Universite de Paris, 8, 229-231.

13.
Umberto, C. L. and Walter, V. (2004). Copula Methods in Finance, Wiley.

14.
Zangari, P. (1996). An Improved Methodology for Measuring VaR, RiskMetrics Monitor, 2, 7-25.