Modelling Security Market Events in Continuous Time: Intensity Based, Multivariate Point Process Models

A continuous time econometric modelling framework for multivariate financial market event (or 'transactions') data is developed in which the model is specified via the vector conditional intensity. This has the advantage that the conditioning information set is updated continuously in time as new information arrives. Generalised Hawkes (g-Hawkes) models are introduced that are sufficiently flexible to incorporate `inhibitory' events and dependence between trading days. Novel omnibus specification tests for parametric models based on a multivariate random time change theorem are proposed. A computationally efficient thinning algorithm for simulation of g-Hawkes processes is also developed. A continuous time, bivariate point process model of the timing of trades and mid-quote changes is presented for a New York Stock Exchange stock and the empirical findings are related to the market microstructure literature. The two-way interaction of trades and quote changes is found to be important empirically. Furthermore, the model delivers a continuous record of instantaneous volatility that is conditional on the timing of trades and quote changes.