Dynamic Discrete Mixtures for High Frequency Prices

39 Pages Posted: 1 Apr 2019

See all articles by Leopoldo Catania

Leopoldo Catania

Aarhus University - School of Business and Social Sciences; Aarhus University - CREATES

Roberto Di Mari

University of Catania - Department of Economics and Quantitative Methods

Paolo Santucci de Magistris

LUISS Guido Carli University

Date Written: March 8, 2019

Abstract

The tick structure of the financial markets entails that price changes observed at very high frequency are discrete. Departing from this empirical evidence we develop a new model to describe the dynamic properties of multivariate time-series of high frequency price changes, including the high probability of observing no variations (price staleness). We assume the existence of two independent latent/hidden Markov processes determining the dynamic properties of the price changes and the excess probability of the occurrence of zeros. We study the probabilistic properties of the model that generates a zero-inflated mixture of Skellam distributions and we develop an EM estimation procedure with closed-form M step. In the empirical application, we study the joint distribution of the price changes of four assets traded on NYSE. Particular focus is dedicated to the precision of the univariate and multivariate density forecasts, to the quality of the predictions of quantities like the volatility and correlations across assets, and to the possibility of disentangling the different sources of zero price variation as generated by absence of news, microstructural frictions or by the offsetting positions taken by the traders.

Keywords: Dynamic Mixtures, Skellam Distribution, Zero-Inflated Series, EM Algorithm, High Frequency Prices, Volatility

JEL Classification: C38, C60, G13

Suggested Citation

Catania, Leopoldo and Di Mari, Roberto and Santucci de Magistris, Paolo, Dynamic Discrete Mixtures for High Frequency Prices (March 8, 2019). Available at SSRN: https://ssrn.com/abstract=3349118 or http://dx.doi.org/10.2139/ssrn.3349118

Leopoldo Catania (Contact Author)

Aarhus University - School of Business and Social Sciences ( email )

Fuglesangs Allé 4
Aarhus V, DK-8210
Denmark
+4587165536 (Phone)

HOME PAGE: http://pure.au.dk/portal/en/leopoldo.catania@econ.au.dk

Aarhus University - CREATES ( email )

School of Economics and Management
Building 1322, Bartholins Alle 10
DK-8000 Aarhus C
Denmark

Roberto Di Mari

University of Catania - Department of Economics and Quantitative Methods ( email )

Corso Italia, 55
95129 Catania
Italy

HOME PAGE: http://www.datasciencegroup.unict.it/content/roberto-di-mari

Paolo Santucci de Magistris

LUISS Guido Carli University ( email )

Via O. Tommasini 1
Rome, Roma 00100
Italy

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