Modeling Price and Variance Jump Clustering Using the Marked Hawkes Process*

We examine the clustering behavior of price and variance jumps using high-frequency data, modeled as a marked Hawkes process (MHP) embedded in a bivariate jump-diffusion model with intraday periodic effects. We find that the jumps of both individual stocks and a broad index exhibit self-exciting behavior. The three dimensions of the model, namely positive price jumps, negative price jumps, and variance jumps, impact one another in an asymmetric fashion. We estimate model parameters using Bayesian inference by Markov Chain Monte Carlo, and find that the inclusion of the jump parameters improves the fit of the model. When we quantify the jump intensity and study the characteristics of jump clusters, we find that in high-frequency settings, jump clustering can last between 2.5 and 6 hours on average. We also find that the MHP generally outperforms other models in terms of reproducing two cluster-related characteristics found in the actual data.