Analyzing order flows in limit order books with ratios of Cox-type intensities

Abstract

We introduce a Cox-type model for relative intensities of order flows in a limit order book. The model assumes that all intensities share a common baseline intensity, which may for example represent the global market activity. Parameters can be estimated by quasi-likelihood maximization, without any interference from the baseline intensity. Consistency and asymptotic behavior of the estimators are given in several frameworks, and model selection is discussed with information criteria and penalization. The model is well-suited for high-frequency financial data: fitted models using easily interpretable covariates show an excellent agreement with empirical data. Extensive investigation on tick data consequently helps identifying trading signals and important factors determining the limit order book dynamics. We also illustrate the potential use of the framework for out-of-sample predictions.

Keywords:

• Order book models
• Point processes
• Cox processes
• Hawkes processes
• Ratio models
• Trading signals
• Imbalance
• Spread

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Ioane Muni Toke  http://orcid.org/0000-0002-0283-8179

Notes

† Removing the beginning and the trading day has been done as a usual precautionary step when dealing with high-frequency trades and quotes databases, as one may sometimes be concerned with data quality in very busy periods. However, this precaution may actually not be necessary. For example, when recomputing figure 4 using the whole trading day, we observe no significant visual difference with the version presented in this paper.

Additional information

Funding

This work was in part supported by Japan Science and Technology Agency Core Research for Evolutional Science and Technology (CREST) JPMJCR14D7; Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research No. 17H01702 (Scientific Research), No. 26540011 (Challenging Exploratory Research); and by a Cooperative Research Program of the Institute of Statistical Mathematics.