An Inflated Multivariate Integer Count Hurdle Model: An Application to Bid and Ask Quote Dynamics

Abstract

In this paper we develop a model for the conditional inflated multivariate density of integer count variables with domain Z^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 kind of properties can be found for high or ultra-high frequent data describing the trading process on financial markets. We present a straightforward method of sampling from 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.

Keywords: Multivariate Discrete Distributions, Conditional Inflation, Copula Functions, Truncations, Metropolized-Independence Sampler

JEL Classification: G10, F30, C30