Time-changed GARCH versus the GARJI model for prediction of extreme news events: An empirical study

Chan and Maheu (2002) developed a GARCH-jump mixture model, namely, the GARCH-jump with autoregressive conditional jump intensity (GARJI) model, in which two conditional independent processes, i.e., a diffusion and a compounded Poisson process, are used to describe stock price movements caused by normal and extreme news events, respectively. The resulting model specifically accounts for the volatility clustering and leverage effect, however, it is over-parameterized and provides only an ex post filter for the probability of large price movements occurring. This study proposes and calibrates a more informative and parsimonious model, the VG NGARCH model. Being an extension of the variance-gamma model developed by Madan, Carr, and Chang (1998), the proposed VG NGARCH model imposes an autoregressive structure on the conditional shape parameters, which describes the arrival rates for news with different degrees of impact on price movements, and provides an ex ante probability for the occurrences of large price movements. The performance of the proposed VG NGARCH model is compared with that of the GARJI model using daily stock prices of five financial companies contained in the S&P 500, namely, Bank of America, Wells Fargo, J.P. Morgan Chase, CitiGroup, and AIG, from January 3, 2006 to December 31, 2009. The goodness of fit of the VG NGARCH model and its ability to predict the probabilities of large price movements are demonstrated by comparison with the benchmark GARJI model.