Time-Changed GARCH versus GARJI Model for Extreme Events: An Empirical Study

In literature, a GARCH-jump mixture model, namely, the GARCH-jump model 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 account for stock price movements caused by normal and extreme event news arrivals, individually, is developed by Chan and Maheu (2002, 2004) to describe the volatility clustering and leverage effect phenomenon. The resulting model is less efficient and provides only ex post filter for the probability of the occurrences of large price movements. A more informative and parsimonious model, however, the VG NGARCH model, is proposed and calibrated in this study. Being an extension of the variance-gamma model developed by Madan et al. (1998), the proposed VG NGARCH model incorporates an autoregressive structure on the conditional shape parameters, which describes the news arrival rates of different impact sizes on the price movements, and an ex ante prediction for the occurrences of large price movements is provided. The performance of the proposed VG NGARCH model is compared to the GARJI model based on daily stock prices of five component financial companies in S&P 500, namely, Bank of America, Wells Fargo, J.P. Morgan Chase, CitiGroup, and AIG, respectively, 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 comparing with the benchmark GARJI model.