An inflated multivariate integer count hurdle model: an application to bid and ask quote dynamics

Abstract

Abstract In this paper we develop a model for the conditional inflated multivariate density of integer count variables with domain ℤ n , n ∈ ℕ . Our modelling framework is based on a copula approach and can be used for a broad set of applications where the primary characteristics of the data are: (i) discrete domain; (ii) the tendency to cluster at certain outcome values; and (iii) contemporaneous dependence. These kinds of properties can be found for high‐ or ultra‐high‐frequency data describing the trading process on financial markets. We present a straightforward sampling method for such an inflated multivariate density through the application of an independence Metropolis–Hastings sampling algorithm. We demonstrate the power of our approach by modelling the conditional bivariate density of bid and ask quote changes in a high‐frequency setup. We show how to derive the implied conditional discrete density of the bid–ask spread, taking quote clusterings (at multiples of 5 ticks) into account. Copyright © 2009 John Wiley & Sons, Ltd.