A vg-ngarch model for impacts of extreme events on stock returns

Abstract

This article compares two types of GARCH models, namely, the VG-NGARCH and the GARCH-jump model with autoregressive conditional jump intensity, i.e., the GARJI model, to make inferences on the log of stock returns when there are irregular substantial price fluctuations. The VG-NGARCH model imposes a nonlinear asymmetric structure on the conditional shape parameters in a variance-gamma process, which describes the arrival rates for news with different degrees of influence on price movements and provides an ex ante probability for the occurrence of large price movements. On the other hand, the GARJI model, a mixed GARCH-jump model proposed by Chan and Maheu (Journal of Business & Economic Statistics 20:377-389, 2002), adopts two independent autoregressive processes to model the variances corresponding to moderate and large price movements, respectively. An empirical study using daily stock prices of four major banks, namely, Bank of America, J.P. Morgan Chase, Citigroup, and Wells Fargo, from 2006 to 2009 is performed to compare the two models. The goodness of fit of the VG-NGARCH model vs. the GARJI model is demonstrated.