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

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. The calculation of marginal likelihoods for the proposed and related models is discussed. An extensive empirical investigation is undertaken using the S&P500 market index, with substantial support for dynamic jump intensities – including in terms of predictive accuracy – documented.