A comment on Christoffersen, Jacobs, and Ornthanalai (2012), “Dynamic jump intensities and risk premiums: Evidence from S&P 500 returns and options”

Christoffersen, Jacobs, and Ornthanalai (2012) (CJO) propose an interesting and useful class of generalized autoregressive conditional heteroskedasticity (GARCH)-like models with dynamic jump intensity, and find evidence that the models not only fit returns data better than some commonly used benchmarks but also provide substantial improvements in option pricing performance. While such models pose difficulties for estimation and analysis, CJO propose an innovative approach to filtering intended to addresses them. However, some statistical issues arise that their approach leaves unresolved, with implications for the option pricing results. This note proposes a solution based on using the filter and estimator proposed by CJO but interpreted in the context of an alternative model. With respect to this model, the estimator is consistent, and likelihood-based model comparisons and hypothesis tests are valid.