Performance Of GARCH-EVT And Vine Copula In Modeling Extreme Dependence And Estimation Of Value-at-Risk

Dependence modeling and estimation of Value-at-Risk are vital concepts in financial risk management. However, it is important to note that the validity and accuracy of VaR highly depends on the distribution assumption of the financial returns under study. This thesis therefore evaluates the effectiveness of using GARCH-EVT and Vine-Copula in modeling dependence in extreme financial returns andthe estimation of value at risk (VaR). In both cases, the returns are first filtered using GARCH-type models before the Extreme Value analysis.For the Value at Risk (VaR) estimation, the inference function for margin (IFM) approach is used in the analysis, where the estimation is done in two stages. The first stage is the modeling of the marginal distributions. This is done using the semi-parametric method, where the peak-over threshold (POT) approach is used to model the tails of each residual series (parametric) and the center of each series modeled empirically using kernel smoothing (non-parametric). The second stage of the IFM is the dependence modeling. This is done using vine copula with pair-copula as building blocks. For comparison, other methods of VaR estimation are also considered. The performance of the proposed method relative to the other methods is assessed based on the out of sample performance of each method as indicated by the VaR and ES backtest results.For the dependence modeling of extremes (Extreme gains and Losses) using Vine-Copula, The peak over threshold approach is use to identify the sets of extreme gains and extreme losses in each asset contain in the portfolio. Three assets are considered for the dependence modeling. For the three assets considered, a total of six data sets (3sets of extreme gains and3sets of extreme losses) are use in the dependence modeling. Between the two special classes (C-and D-vine) of vine copula models, the best model for the dependence modeling is chosen base on statistical tests.For the estimation of VaR, empirical evidence base on the backtest results shows that the GARCH-EVT approach using Mix D-vine copula model with semiparametric margins outperforms all the other models, as it passed both the conditional and unconditional coverage tests with the least number of VaR violation for both upper and lower tails at the1%and5%significance levels.For the dependence modeling, Empirical evidence (base on data) shows that, the C-vine copula is more appropriate for modeling the dependence in the extremes.The dependence parameters for the upper and lower tails are negative for most pairs.This shows that, some form of dependence relationships exist between pairs of tails in the portfolio that worth knowing for good management planning.