A Comparison of GARCH Models for VAR Estimation

This study is an attempt to compare a comprehensive list of GARCH models in quantifying risks of VaR under stress times. We gather data of stock market indices from both emerging (Brazil and Turkey) and developed (Germany and the USA) markets, over the period of global financial crisis and make use of numerous GARCH specifications to return VaR values. Then we compare the assessments of VaR with the realized returns by Kupiec and Christoffersen Tests. Besides, we calculate Quadratic Losses to evaluate the GARCH specifications in calculating VaR. The results reveal that the ARCH specification is the best performer followed by GARCH(1, 1) and the Student’s t distribution is slightly better than the Normal. The other outcome of the paper is that the worst performers are Non-Linear Power GARCH and Non-Linear Power GARCH with a shift. All GARCH estimations are carried out with STATA that uses the Maximum Likelihood method of estimation