Abstract
This paper extends the analysis of Muni Toke and Yoshida (2020) to the case of marked point processes. We consider multiple marked point processes with intensities defined by three multiplicative components, namely a common baseline intensity, a state-dependent component specific to each process, and a state-dependent component specific to each mark within each process. We show that for specific mark distributions, this model is a combination of the ratio models defined in Muni Toke and Yoshida (2020). We prove convergence results for the quasi-maximum and quasi-Bayesian likelihood estimators of this model and provide numerical illustrations of the asymptotic variances. We use these ratio processes to model transactions occurring in a limit order book. Model flexibility allows us to investigate both state-dependency (emphasizing the role of imbalance and spread as significant signals) and clustering. Calibration, model selection and prediction results are reported for high-frequency trading data on multiple stocks traded on Euronext Paris. We show that the marked ratio model outperforms other intensity-based methods (such as “pure” Hawkes-based methods) in predicting the sign and aggressiveness of market orders on financial markets.
Highlights
The limit order book is the central structure that aggregates buy and sell intentions of all the market participants on a given exchange
Hawkes processes have been successfully suggested for the modeling of limit order book events (Bowsher 2007; Large 2007; Bacry et al 2012, 2013; Muni Toke and Pomponio 2012; Lallouache and Challet 2016; Lu and Abergel 2018)
We extend the framework of Muni Toke and Yoshida (2020) to some cases of marked point processes, by adding a third term to the multiplicative definition of the intensity, which accounts for some mark distribution
Summary
The limit order book is the central structure that aggregates buy and sell intentions of all the market participants on a given exchange. Hawkes processes have been successfully suggested for the modeling of limit order book events (Bowsher 2007; Large 2007; Bacry et al 2012, 2013; Muni Toke and Pomponio 2012; Lallouache and Challet 2016; Lu and Abergel 2018) One drawback of such models is the difficulty to account for high intraday variability. We extend the framework of Muni Toke and Yoshida (2020) to some cases of marked point processes, by adding a third term to the multiplicative definition of the intensity, which accounts for some mark distribution We use this extension to deepen our investigation of limit order book data.
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