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

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.