Overestimation in the Traditional GARCH Model During Jump Periods

The traditional continuous and smooth models, like the GARCH model, may fail to capture extreme returns volatility. Therefore, this study applies the bivariate poisson (CBP)-GARCH model to study jump dynamics in price volatility of crude oil and heating oil during the past 20 years. The empirical results indicate that the variance and covariance of the GARCH and CBP-GARCH models were found to be similar in low jump intensity periods and to diverge during jump events. Significant overestimations occur during high jump time periods in the GARCH model because of assumptions of continuity, and easily leading to excessive hedging and overly measuring risk. Nevertheless, in the CBP-GARCH model, the specific shocks are assumed to be independent of normal volatility and to reduce the persistence of abnormal volatility. Therefore, the CBP-GARCH model is appropriate and necessary in high volatility markets.