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http://dx.doi.org/10.5351/KJAS.2016.29.4.753

Performance analysis of EVT-GARCH-Copula models for estimating portfolio Value at Risk  

Lee, Sang Hun (Department of Applied Statistics, Konkuk University)
Yeo, Sung Chil (Department of Applied Statistics, Konkuk University)
Publication Information
The Korean Journal of Applied Statistics / v.29, no.4, 2016 , pp. 753-771 More about this Journal
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.
Keywords
Value at Risk; extreme value theory; GARCH models; copula; back testing;
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Times Cited By KSCI : 3  (Citation Analysis)
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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.   DOI
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.   DOI
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.   DOI
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.   DOI
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.   DOI
12 Engle, R. F. and Bollerslev, T. (1986). Modeling the persistence of conditional variances, Econometric Reviews, 5, 1-50.   DOI
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.   DOI
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.   DOI
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.   DOI
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.   DOI
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.   DOI
23 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.
24 Longin, F. M. and Solnik, B. (2001). Extreme correlation of international equity markets, Journal of Finance, 56, 649-676.   DOI
25 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.   DOI
26 Poon, S.-H., Rockinger, M., and Tawn, J. (2003). Modeling extreme value dependence in international stock markets, Statistica Sinica, 13, 929-953.
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.   DOI
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.   DOI
31 Zakoian, J. M. (1994). Threshold heteroscedastic models, Journal of Economic Dynamics and Control, 18, 931-955.   DOI