Model Selection for Value-at-risk: Univariate and Multivariate Approaches

Abstract

This thesis sought to determine the best among various models in estimating VaR. Models were evaluated in terms of both accurate probabilities of extreme events and lack of correlation among exceptions. In DJIA index portfolio, the GARCH model with t-distribution and the HS model were not rejected in both tails. This result makes sense if we consider the fact that these two models are more robust to the fat-tail characteristic of financial time series than the other models. However, in hypothetical portfolio which has fatter tails than the DJIA index portfolio, all other models were rejected. We compared the results using the univariate models. All univariate models and multivariate models could be rejected with the PF test or with the runs test in the left or right tail.However,if we consider only the PF test, the DCC models and the O-GARCH model, were not reject in both tails.