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

In this paper we develop a model for the conditional inflated multivariate density of integer count variables with domain ℤ, 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. [ABSTRACT FROM AUTHOR]