The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Performance analysis of EVT-GARCH-Copula models for estimating portfolio Value at Risk

포트폴리오 VaR 측정을 위한 EVT-GARCH-코퓰러 모형의 성과분석

  • Lee, Sang Hun (Department of Applied Statistics, Konkuk University) ;
  • Yeo, Sung Chil (Department of Applied Statistics, Konkuk University)
  • 이상훈 (건국대학교 응용통계학과) ;
  • 여성칠 (건국대학교 응용통계학과)
  • Received : 2016.04.11
  • Accepted : 2016.05.25
  • Published : 2016.06.30
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Abstract

Value at Risk (VaR) is widely used as an important tool for risk management of financial institutions. In this paper we discuss estimation and back testing for VaR of the portfolio composed of KOSPI, Dow Jones, Shanghai, Nikkei indexes. The copula functions are adopted to construct the multivariate distributions of portfolio components from marginal distributions that combine extreme value theory and GARCH models. Volatility models with t distribution of the error terms using Gaussian, t, Clayton and Frank copula functions are shown to be more appropriate than the other models, in particular the model using the Frank copula is shown to be the best.

금융기관의 위험관리를 위한 중요한 도구로서 현재 VaR가 널리 사용되고 있다. 본 논문에서는 코퓰러 함수들을 이용하여 극단치이론과 GARCH 모형을 결합한 일변량분포로부터 구축한 다변량분포들을 바탕으로 코스피, 다우존스, 상하이 그리고 니케이 지수들로 구성된 포트폴리오의 VaR 추정과 그 성과에 관해 논의하였다. 사후검증 결과 전체적으로 볼 때 가우시안, t, 클레이톤, 프랭크 코퓰러를 사용한 t-분포의 오차항을 가진 변동성 모형들이 포트폴리오 VaR의 측정에 적합한 모형들로 나타났으며, 특히 프랭크 코퓰러의 경우에 가장 우수한 성과를 나타내었다.

Keywords

References

  1. Alexander, C. (2008). Market Risk Analysis IV: Value at Risk Models, John Wiley & Sons, England.
  2. Black, F. (1976). Studies of stock market volatility changes. In Proceedings of the American Statistical Association, Business and Economic Statistics Section, 177-181.
  3. Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity, Journal of Econometrics, 31, 307-327. https://doi.org/10.1016/0304-4076(86)90063-1
  4. Cherubini, U., Luciano, E., and Vecchiato, W. (2004). Copula Methods in Finance, John Wiley & Sons, England.
  5. Christoffersen, P. F. (1998). Evaluating interval forecasts, International Economic Review, 39, 841-864. https://doi.org/10.2307/2527341
  6. Danielsson, J. and de Vries, C. G. (1997). Tail index and quantile estimation with very high frequency data, Journal of Empirical Finance, 4, 241-257. https://doi.org/10.1016/S0927-5398(97)00008-X
  7. Danielsson, J. and de Vries, C. G. (2000). Value-at-risk and extreme returns, Annales d'Economie et de Statistique, 60, 239-270.
  8. Ding, Z., Granger, C. W. J., and Engle, R. F. (1993). A long memory property of stock market returns and model, Journal of Empirical Finance, 1, 83-106. https://doi.org/10.1016/0927-5398(93)90006-D
  9. Dowd, K. (1998). Beyond value at Risk: The new Science of Risk Management, John Wiley & Sons, England.
  10. Embrechts, P., McNeil, A. J., and Straumann, D. (1999). Correlation: pitfalls and alternatives, Risk, 5, 69-71.
  11. Engle, R. F. (1982). Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation, Econometrica, 50, 987-1006. https://doi.org/10.2307/1912773
  12. Engle, R. F. and Bollerslev, T. (1986). Modeling the persistence of conditional variances, Econometric Reviews, 5, 1-50. https://doi.org/10.1080/07474938608800095
  13. Ghorbel, A. and Trabelsi, A. (2009). Measure of financial risk using conditional extreme value copulas with EVT margins, Journal of Risk, 11, 51-85. https://doi.org/10.21314/JOR.2009.196
  14. Glosten, L. R., Jaganathan, R., and Runkle, D. E. (1993). On the relation between the expected value and the volatility of the nominal excess return on stocks, Journal of Finance, 48, 1779-1801. https://doi.org/10.1111/j.1540-6261.1993.tb05128.x
  15. Huang, S.-C., Chien, Y.-H., and Wang, R.-C. (2011). Applying GARCH-EVT-Copula models for portfolio Value-at-Risk on G7 currency markets, International Research Journal of Finance and Economics, 74, 136-151.
  16. Hsu, C.-P., Huang, C.-W., and Chiou, W.-J. P. (2011). Effectiveness of copula-extreme value theory in estimating Value-at-Risk: empirical evidence from Asian emerging markets, Review of Quantitative Finance and Accounting, 39, 447-468
  17. Joe, H. (1997). Multivariate Models and Dependence Concepts, Chapman and Hall, London.
  18. Jorion, P. (2007). Value at Risk (3rd Ed), McGraw Hill, New York.
  19. Kupiec, P. (1995). Techniques for verifying the accuracy of risk measurement models, Journal of Derivatives, 2, 73-84. https://doi.org/10.3905/jod.1995.407918
  20. Lee, S. H. (2016). Performance Analysis of VaR estimates using EVT-GARCH-Copula model, Master Thesis, Konkuk University, Seoul.
  21. Longin, F. M. (1996). The asymptotic distribution of extreme stock market returns, Journal of Business, 69, 383-408. https://doi.org/10.1086/209695
  22. Longin, F. M. (2000). From Value at Risk to stress testing: the extreme value approach, The Journal of Banking and Finance, 24, 1097-1130. https://doi.org/10.1016/S0378-4266(99)00077-1
  23. Longin, F. M. and Solnik, B. (2001). Extreme correlation of international equity markets, Journal of Finance, 56, 649-676. https://doi.org/10.1111/0022-1082.00340
  24. McNeil, A. J. and Frey, R. (2000). Estimation of tail-related risk for heteroscedastic financial time series: an extreme value approach, Journal of Empirical Finance, 7, 271-300. https://doi.org/10.1016/S0927-5398(00)00012-8
  25. Poon, S.-H., Rockinger, M., and Tawn, J. (2003). Modeling extreme value dependence in international stock markets, Statistica Sinica, 13, 929-953.
  26. Sklar, A. (1959). Fonctions de repartition a n dimensions et leurs marges, Publications de l'Institut de Statistique de l'Universite de Paris, 8, 229-231.
  27. Taylor, S. J. (1986). Modelling Financial Time Series, John Wiley & Sons, London.
  28. Yeo, S. C. (2006a). Performance analysis of VaR and ES based on extreme value theory, The Korean Communications in Statistics, 13, 389-407.
  29. Yeo, S. C. (2006b). Estimation and performance analysis of risk measures using copula and extreme value theory, The Korean Journal of Applied Statistics, 19, 481-504. https://doi.org/10.5351/KJAS.2006.19.3.481
  30. Yeo, S. C. and Li, Z. (2015). Performance analysis of volatility models for estimating portfolio Value at Risk, The Korean Journal of Applied Statistics, 28, 541-559. https://doi.org/10.5351/KJAS.2015.28.3.541
  31. Zakoian, J. M. (1994). Threshold heteroscedastic models, Journal of Economic Dynamics and Control, 18, 931-955. https://doi.org/10.1016/0165-1889(94)90039-6