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Title: Microstructure of foreign exchange market: Cox vs. Hawkes process Authors:  Nuria Ruiz-Fuentes - University of Jaen (Spain) [presenting]
Francisco Luguera - Universidad de Granada (Spain)
Paula Bouzas - University of Granada (Spain)
Abstract: The microstructure of the foreign exchange market is obviously an important field within the financial sphere; additionally, from the statistical point of view, it provides many examples of high-intensity counting processes. One such example is the number of changes of the bid and ask prices on the EUR/USD currency pair when observed in milliseconds. The Hawkes process is widely used in the literature to model this data. The intensity was calculated considering different regularization and optimization methods deriving a good model; nevertheless, the model does not provide important outcomes, such as predictions within a future interval of time. Therefore, the Cox process with intensity process modelled by FDA was considered as a worthwhile alternative to explore. In this case, having chosen the interval of time to model, less data was required to apply the estimation method, and the intensity process was stochastically estimated. Finally, the Cox process produced low error predictions and used a short processing time.