Modeling High-Frequency Non-Homogeneous Order Flows by Compound Cox Processes*
- Autores: Chertok A.1,2, Korolev V.1,3, Korchagin A.1
-
Afiliações:
- Lomonosov Moscow State University
- Euphoria Group LLC
- Institute of Informatics Problems of RAS
- Edição: Volume 214, Nº 1 (2016)
- Páginas: 44-68
- Seção: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/237319
- DOI: https://doi.org/10.1007/s10958-016-2757-6
- ID: 237319
Citar
Resumo
A micro-scale model is proposed for the evolution of a limit order book in modern high-frequency trading applications. Within this model, order flows are described by doubly stochastic Poisson processes (also called Cox processes) taking account of the stochastic character of the intensities of order flows. The models for the number of order imbalance (NOI) process and order flow imbalance (OFI) process are introduced as two-sided risk processes that are special compound Cox processes. These processes are sensitive indicators of the current state of the limit order book since time intervals between events in a limit order book are usually so short that price changes are relatively infrequent events. Therefore price changes provide a very coarse and limited description of market dynamics at time micro-scales. NOI and OFI processes track best bid and ask queues and change much faster than prices. They incorporate information about build-ups and depletions of order queues and they can be used to interpolate market dynamics between price changes and to track the toxicity of order flows. 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 without modeling the external information background. The proposed model gives the opportunity to link the micro-scale high-frequency 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 for special random sums and hence, to give a deeper insight in the nature of popular models of statistical regularities of the evolution of characteristics of financial markets such as generalized hyperbolic distributions and other normal variance-mean mixtures.
Palavras-chave
Sobre autores
A. Chertok
Lomonosov Moscow State University; Euphoria Group LLC
Autor responsável pela correspondência
Email: a.v.chertok@gmail.com
Rússia, Moscow
V. Korolev
Lomonosov Moscow State University; Institute of Informatics Problems of RAS
Email: a.v.chertok@gmail.com
Rússia, Moscow
A. Korchagin
Lomonosov Moscow State University
Email: a.v.chertok@gmail.com
Rússia, Moscow