Predicting Uncertainty in Financial Markets : -An empirical study on ARCH-class models ability to estimate Value at Risk

Sammanfattning: Value at Risk has over the last couple of decades become one of the most widely used measures of market risk. Several methods to compute this measure have been suggested. In this paper, we evaluate the use of the GARCH(1,1)-, EGARCH(1,1)- and the APARCH(1,1) model for estimation of this measure under the assumption that the conditional error distribution is normally-, t-, skewed t- and NIG-distributed respectively. For each model, the 95% and 99% one-day Value at Risk is computed using rolling out-of-sample forecasts for three equity indices. These forecasts are evaluated with Kupiec´s test for unconditional coverage test and Christoffersen’s test for conditional coverage. The results imply that the models generally perform well. The APARCH(1,1) model seems to be the most robust model. However, the GARCH(1,1) and the EGARCH(1,1) models also provide accurate predictions. The results indicate that the assumption of conditional distribution matters more for 99% than 95% Value at Risk. Generally, a leptokurtic distribution appears to be a sound choice for the conditional distribution.