A Comparative Study of GARCH and EVT Model in Modeling Value-at-Risk

Abstract

The paper addresses an inefficiency of the traditional approach in modeling the tail risk, particularly the 1-day ahead forecast of Value-at-Risk (VaR), using Extreme Value Theory (EVT) and GARCH model. Specifically, I apply both models onto major countries stock markets daily loss, including U.S., U.K., China and Hong Kong between 2006 and 2015, and compare the relative forecasting performance. The paper differs from other studies in two important ways. First, it incorporates an asymmetric shock of volatility in the financial time series. Second, it applies a skewed fat-tailed return distribution using the Generalized Error Distribution (GED). The back-testing result shows that, on one hand, the conditional EVT performs equally well relative to GARCH model under the Generalized Error Distribution. On the other hand, the Exponential GARCH based model is the best performing one in Value-at-Risk forecasting, because it not only correctly identifies the future extreme loss, but more importantly, its occurrence is independent.