Dynamic jumps in the price and volatility of an asset are modelled using a joint Hawkes process in conjunction with a bivariate jump diffusion. A state-space representation is used to link observed returns, plus nonparametric measures of integrated volatility and price jumps, to the specified model components, with Bayesian inference conducted using a Markov chain Monte Carlo algorithm. An evaluation of marginal likelihoods for the proposed model relative to a large number of alternative models, including some that have featured in the literature, is provided. An extensive empirical investigation is undertaken using data on the S&P 500 market index over the 1996-2014 period, with substantial support for dynamic jump intensities-including in terms of predictive accuracy-documented.
