Modeling First Line Of An Order Book With Multivariate Marked Point Processes

Alexis Fauth (1) , Ciprian A. Tudor (2)

1 SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)
2 LPP - Laboratoire Paul Painlevé - UMR 8524

We introduce a new model in order to describe the fluctuation of tick-by-tick financial time series. Our model, based on marked point process, allows us to incorporate in a unique process the duration of the transaction and the corresponding volume of orders. The model is motivated by the fact that the "excitation" of the market is different in periods of time with low exchanged volume and high volume exchanged. We illustrate our result by numerical simulations on foreign exchange data sampling in millisecond. By checking the main stylized facts, we show that the model is consistent with the empirical data. We also find an interesting relation between the distribution of the volume of limited order and the volume of market orders. To conclude, we propose an application to risk management and we introduce a forecast procedure.

Mots clés: trading strategy; Order book; bid-ask spread; market impact; microstructure; multivariate marked Hawkes processes; trading strategy.

Domaines: Finance quantitative [q-fin.CP]; Microstructure des marchés [q-fin.TR]; Statistiques [math.ST]; Théorie [stat.TH]

Alexis Fauth, Ciprian A. Tudor. Modeling First Line Of An Order Book With Multivariate Marked Point Processes. 2012. ⟨hal-00752971⟩