Estimation and filtering by reversible jump MCMC for a doubly stochastic Poisson model for ultra-high-frequency financial data

We propose a modeling framework for ultra-high-frequency data on financial asset price movements. The models proposed belong to the class of the doubly stochastic Poisson processes with marks and allow an interpretation of the changes in price volatility and trading activity in terms of news or information arrival. Assuming that the intensity process underlying event arrivals is unobserved by market agents, we propose a signal extraction (filtering) method based on the reversible jump Markov chain Monte Carlo algorithm. Moreover, given a realization of the price process, inference on the parameters can be performed by appealing to stochastic versions of the EM algorithm. The simulation methods proposed will also be applied to the computation of hedging strategies and derivative prices.