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

Abstract

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. Generalised Hawkes models are introduced that incorporate inhibitory events and dependence between trading days. Sufficient conditions for identification of linear Hawkes models and for stationarity of some new non-linear Hawkes models are derived. Novel omnibus specification tests based on a multivariate random time change theorem are proposed. A computationally efficient thinning algorithm for simulation of generalised Hawkes processes is also developed. A bivariate point process model of the timing of trades and mid-quote changes is presented for a New York Stock Exchange stock and related to the market microstructure literature. The two-way interaction of trades and quote changes is found to be important empirically.

Keywords: point process, conditional intensity, Hawkes process, specification test, random time change, transactions data, market microstructure

JEL Classification: C32, C51, C52, G10