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

Ioane Muni Toke (1) , Nakahiro Yoshida (2)

1 MICS - Mathématiques et Informatique pour la Complexité et les Systèmes
2 Graduate school of mathematics

We introduce a Cox-type model for relative intensities of orders 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. Several illustrations are provided.

Keywords: order book models; point processes; Cox model; spread; imbalance; ratio model; trading signals; Cox processes; Hawkes processes; ratio models

Domains: Statistical Finance [q-fin.ST]; Trading and Market Microstructure [q-fin.TR]

Ioane Muni Toke, Nakahiro Yoshida. Analyzing order flows in limit order books with ratios of Cox-type intensities. Quantitative Finance, 2020, 20 (1), pp.81-98. ⟨10.1080/14697688.2019.1637927⟩. ⟨hal-01799398v3⟩