Calculating Value at Risk: DCC-GARCH-Copula Approach

In this paper, in order to calculate portfolio market risk of 10 selected industries indices in Tehran Stock Exchange, two models of Value Risk (VaR) and Expected shortfall (ES) have been used. Different models of multivariate GARCH and various Coppola models have been used in order to estimate the volatility of the portfolio and nonlinear correlation of asset portfolio. Backtesting has been done by Kupiec, Christoffersen, Engle and Manganelli and McNeill and Ferry tests. Results show that the DCC-GARCH model by t-Student distribution compared to other competing models has the best results in estimating volatility of the asset portfolio. Also among all Copula models reviewed in this paper, t-student copula model has shown better results for estimating asset dependence. Finally, the results of backtesting of different models showed that both the DCC-GARCH model with t-Student distribution and DCC-GARCH-Copula with t-Student distribution have acceptable results in estimating VaR and ES. However, the Lopez and Blanco and Ihle tests showed that the DCC-GARCH model with t-Student distribution compared to the DCC-GARCH-Copula model with t-Student distribution gives a more accurate and efficient estimate of the VaR and ES of asset portfolios.