Modeling multivariate ultra-high-frequency financial data by Monte Carlo simulation methods

In this thesis, we propose a modeling framework for multivariate ultra-high-frequency financial data. The proposed models belong to the class of the doubly stochastic Poisson processes with marks which are characterized by the number of events in any time interval to be conditionally Poisson distributed, given another positive stochastic process called intensity. The key assumption of these models is that the intensities are specified through a latent common dynamic factor that jointly drives their common behavior. Assuming the intensities are unobservable, we propose a signal extraction (filtering) method based on the reversible jump Markov chain Monte Carlo algorithm. Our proposed filtering method allows to filter not only the intensities but also their specific and common components. From an empirical stand point, on the basis of a comparison of real data with Monte Carlo simulated data, obtained under different assumptions for ticks (times and logreturns), based mainly on the behavior of the correlation between pairs of assets as a function of the sampling period (Epps effect), we found evidence for the existence of a single latent common factor responsible for the behavior observed in a set of assets from the Borsa di Milano.