Nonlinear filtering using reversible jump Markov chain Monte Carlo in a model for high frequency data

A model for intraday stock price movements is proposed using a doubly stochastic Poisson process with stochastic intensity given by a jump process with drift. In a partial information setting, the filtering of the underlying unobserved intensity driving the times of price changes can be performed by reversible jump Markov chain Monte Carlo simulation. We show an application of the proposed filtering technique to the numerical evaluation of the price of a non redundant contingent claim.