Modelling stock order flows with nonhomogeneous intensities from highfrequency data
Abstract
A microscale model is proposed for the evolution of such information system as the limit order book in financial markets. Within this model, the flows of orders (claims) are described by doubly stochastic Poisson processes taking account of the stochastic character of intensities of buy and sell orders that determine the price discovery mechanism. The proposed multiplicative model of stochastic intensities makes it possible to analyze the characteristics of the order flows as well as the instantaneous proportion of the forces of buyers and sellers, that is, the imbalance process, without modelling the external information background. The proposed model gives the opportunity to link the microscale (highfrequency) dynamics of the limit order book with the macroscale models of stock price processes of the form of subordinated Wiener processes by means of limit theorems of probability theory and hence, to use the normal variancemean mixture models of the corresponding heavytailed distributions. The approach can be useful in different areas with similar properties (e.g., in plasma physics).
 Publication:

11th International Conference of Numerical Analysis and Applied Mathematics 2013: ICNAAM 2013
 Pub Date:
 October 2013
 DOI:
 10.1063/1.4826023
 Bibcode:
 2013AIPC.1558.2394G