Document Type : Original Article


Assistant Professor of Economics, Islamic Azad University, Central Tehran Branch, Tehran, Iran


Value at Risk (VaR) plays a central role in risk management. There are several approaches for the estimation of VaR, such as historical simulation, the variance-covariance and the Monte Carlo approaches. This work presents portfolio VaR using an approach combining Copula functions, Extreme Value Theory (EVT) and GARCH-GJR models. We investigate the interactions between Tehran Stock Exchange Price Index (TEPIX) and Composite NASDAQ Index. We first use an asymmetric GARCH model and an EVT method to model the marginal distributions of each log returns series and then use Copula functions (Gaussian, Student’s t, Clayton, Gumbel and Frank) to link the marginal distributions together into a multivariate distribution. The portfolio VaR is then estimated. To check the goodness of fit of the approach, Backtesting methods are used. The empirical results show that, compared with traditional methods, the copula model captures the value more successfully.


Jondeau, E. Rockinger, M, 2006. The copula-GARCH model of conditional
dependencies: An international stock market application. Journal of International
Money and Finance 25 (5), 827-853.
Ozun, A., Cifter, A., 2007. Portfolio value-at-risk with time-varying copula:
Evidence from the Americans. Marmara University. MPRA Paper No. 2711.
Thomas J. Linsmeier and Neil D. Pearson, 1996, "Risk Measurement: An
Introduction to Value at Risk"
Patton, A. J. (2002). Modelling time-varying exchange rate dependence using the
conditional copula. Working paper, UCSD.
Palaro, H., Hotta, L.K., 2006. Using conditional copulas to estimate value at risk.
Journal of Data Science 4 (1), 93-115.
Jen-Jsung Huang, Kuo-Jung Lee, Hueimei Liang, Wei-Fu Lin, 2009, "Estimating
value at risk"
Engle, R. F. and T. Bollerslev, 1986, "Modeling the persistence of conditional
variances." Econometric Review 5:1–50.
Dias, A., and Embrechts, P. (2003). Dynamic copula models for multivariate highfrequency data in finance. Working Paper, ETH Zurich: Department of
Embrechts, P. and Hoing, A., Juri, A. (2003). Using copula to bound the value-atrisk for functions of dependent risks. Finance and Stochastic 7, 145-167.
Embrechts, P., Lindskog, F. and McNeil, A.J. (2003). Modelling dependence with
copulas and applications to risk management. In Handbook of Heavy Tailed
Distributions in Finance (Edited by S. T. Rachev), 329-384 Elsevier
Wang Z R, Chen X H, Jin Y B and Zhou Y J (2009): '' Estimating risk of foreign
exchange portfolio: Using VaR and CVaR based on GARCH-EVT-Copula
model''. Physica A: Statistical Mechanics and its Applications 389 (21), 4918-
Palaro, P. Hender, Hotta, K. Luiz, '' Using Conditional Copula to Estimate Valueat-Risk''. Journal of Data Science 4(2006), 93-115.
Ngoga Kirabo Bob (2013):''Value at Risk Estimation. A GARCH-EVT-Copula
Approach''. Master thesis of Mathematic and Statistic, University of