THE APPLICATION OF EVT-GARCH-COPULA MODEL FOR THE ESTIMATION OF VaR OF A PORTFOLIO

Copula models have increasingly become popular for modeling the dependence structure of financial risks. This is due to the fact that, in contrast to linear correlation, a copula can model the complete linear and non-linear dependence structure of a multivariate distribution.To estimate the Value-at-Risk (VaR) of a portfolio, one can model the univariate marginal of the risk positions by parametric distributions and estimate the dependence structure joining the marginal by a copula-model in a separate step. Important problems connected with Extreme Value Theory (EVT)- GARCH-Copula models are the question of selecting an appropriate parametric copula for modeling the dependence structure and the problem of testing the goodness-of-fit of the selected model. The objective of this study is to answer the following question. Is EVT-GARCH-Copula models offer a significant improvement over classical correlation-based Value-at-Risk models?. To answer this question the daily index of JKSE index and KLSE index are used to construct a bivariate portfolio. The indexes are recorded during the period of 30 May 2008 to 30 May 2013 consisting of 1270 trading days. The methods of applying EVT-GARCHcopula are as follows: First AR(1)-GARCH(1,1) is applied to filter the data to produce iid (independent identically distributed) data. Then the standardized data are modeled by EVT-Pareto Tail Distribution, next copula functions are used to calibrate the iid data. The backtesting using a total of 700 simulated portfolio shows that tcopula model yield considerably better VaR estimate than the correlation-based model. Moreover, the results show that the elliptical yield the best results.