On the Study of Two Models for Integer-Valued High-Frequency Data

Abstract

Financial prices are usually modelled as continuous, often involving geometric Brownian motion with drift, leverage and possibly jump components. An alternative modelling approach allows financial observations to take integer values that are multiples of a fixed quantity, the ticksize - the monetary value associated with a single change during the price evolution. In the case of high-frequency data, the sample exhibits diverse trading operations in a few seconds. In this context, the observables are assumed to be conditionally independent and identically distributed from either of two flexible likelihoods: the Skellam distribution - defined as the difference between two independent Poisson distributions - or a mixture of Geometric distributions. Posterior inference is obtained via adaptive Gibbs sampling algorithms. Comparisons of the models applied to high-frequency financial data is provided.