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VaR Estimation with Multiple Copula Functions

다차원 Copula 함수를 이용한 VaR 추정

  • Hong, Chong-Sun (Department of Statistics, Sungkyunkwan University) ;
  • Lee, Won-Yong (Research Institute of Applied Statistics, Sungkyunkwan University)
  • 홍종선 (성균관대학교 통계학과) ;
  • 이원용 (성균관대학교 응용통계연구소)
  • Received : 20110600
  • Accepted : 20110900
  • Published : 2011.10.31

Abstract

VaR(Value at risk) is a measure of market risk management and needs to be estimated for multiple distributions. In this paper, Copula functions are used to generate distributions of multivariate random variables. The dependence structure of random variables is classified by the exchangeable Copula, fully nested Copula, partially nested Copula. For the earning rate data of four Korean industries, the parameters of the Archimedean Copula functions including Clayton, Gumbel and Frank Copula are estimated by using three kinds of dependence structure. These Copula functions are then fitted to to the data so that corresponding VaR are obtained and explored.

VaR는 투자목적이나 위험관리수단으로 시장위험을 측정하는 방법으로 현실생활에서는 다변량 분포에 대하여 추정을 필요로 한다. 본 연구는 다변량 확률변수들의 분포를 생성하기 위하여 Copula 함수를 사용한다. 확률변수들의 종속구조를 exchangeable Copula, fully nested Copula, partially nested Copula로 구별하여 토론한다. 국내의 네 종류의 산업체의 수익률 자료를 실증예제로 하여 Clayton, Gumbel, Frank Copula 함수가 포함된 Archimedean Copula 함수의 모수들을 세 종류의 종속구조를 이용하여 구하고, 이 자료에 적합한 Copula 함수와 각 함수에 대응하는 VaR를 추정하고 비교탐색한다.

References

  1. 김명직, 신성환 (2003). Copula 함수의 추정과 시뮬레이션, <선물연구>, 11, 103-131.
  2. 김철중 (2001). VaR 측정의 기본원리, <금융>, 567, 44-49.
  3. 여성칠 (2006). 코퓰러와 극단치이론을 이용한 위험척도의 추정 및 성과분석, <응용통계연구>, 19, 481-504. https://doi.org/10.5351/KJAS.2006.19.3.481
  4. 홍종선, 권태완 (2010). 수익률분포의 적합과 리스크값 추정, <한국데이터정보과학회지>, 21, 219-229.
  5. 홍종선, 이재형 (2011). Copula 함수를 이용한 이변량분포의 VaR 추정, <응용통계연구>, 게재예정. https://doi.org/10.5351/KJAS.2011.24.3.523
  6. 황수영 (2005). , 한국과학기술원, 박사학위논문.
  7. Bae, K. H. and Karolyi, A. (2003). A new approach to measuring financial contagion, Review of Financial Studies, 16, 717-763. https://doi.org/10.1093/rfs/hhg012
  8. Breymann, W. (2003). Dependence structures for multivariate high-frequency data in finance, Quantitative Finance, 3, 1-14. https://doi.org/10.1080/713666155
  9. Dobric, J. and Schmid, F. (2005). Nonparametric estimation of the lower tail dependence in bivariate copulas, Journal of Applied Statistics, 32, 387-407. https://doi.org/10.1080/02664760500079217
  10. Embrechts, P., McNeil, A. J. and Straumann, D. (1999). Correlation: Pitfalls and alternatives, Risk, 5, 69-71.
  11. Genest, C., Ghoudi, K. and Rivest, L. P. (1995). A semiparametric estimation procedure of dependence parameters in multivariate families of distributions, Biometrika, 82, 543-552. https://doi.org/10.1093/biomet/82.3.543
  12. Joe, H. (2005). Asymptotic efficiency of the two-stage estimation method for copulabased models, Journal of Multivariate Analysis, 94, 401-419. https://doi.org/10.1016/j.jmva.2004.06.003
  13. Jorion, P. (1997). Value at Risk, McGraw-Hill, New York.
  14. Li, D. X. (1999). Value at Risk based on the Volatility Skewness and Kurtosis, RiskMetrics Group.
  15. Longin, S. (2001). Extreme correlation of international equity markets, The Journal of Finance, 2, 649-676.
  16. Marshal, R. and Zeevi, A. (2002). Beyond Correlation: Extreme Co-movements between Financial Assets, Working paper, Columbia Business School.
  17. McNeil, A. J. (2008). Sampling nested archimedean copulas, Journal of Statistical Computation and Simulation, 6, 567-581.
  18. Nelson, R. B. (2006). An Introduction to Copula, 6th Edition, Springer.
  19. Savu, C. and Trede, M. (2006). Hierarchical archimedean copulas, International Conference on High Frequency Finance, Konstanz.
  20. Shih, J. and Louis, T. (1995). Inferences on the association parameter in copula models for bivariate survival data, Biometrics, 51, 1384-1399. https://doi.org/10.2307/2533269
  21. Sklar, A. (1959). Fonctions de repartition a n dimensions et leurs marges, l'Institut de Statistique de L'Universite de Paris, 8, 229-231.
  22. Umberto, C. L. and Walter, V. (2004). Copula Methods in Finance, Wiley.
  23. Zangari, P. (1996). An improved methodology for measuring VaR, RiskMetrics Monitor, 2, 7-25.

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