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Dynamic jumps in the price and volatility of an asset are modelled using ajoint Hawkes process in conjunction with a bivariate jump diffusion. A statespace representation is used to link observed returns, plus nonparametricmeasures of integrated volatility and price jumps, to the specified modelcomponents; with Bayesian inference conducted using a Markov chain Monte Carloalgorithm. An evaluation of marginal likelihoods for the proposed modelrelative to a large number of alternative models, including some that havefeatured in the literature, is provided. An extensive empirical investigationis undertaken using data on the S&P500 market index over the 1996 to 2014period, with substantial support for dynamic jump intensities - including interms of predictive accuracy - documented.

Inference on Self-Exciting Jumps in Prices and Volatility using High Frequency Measures