This article studies two extensions of the compound Poisson process with iid Gaussian innovations which are able to characterize important features of high frequency security prices. The first model explicitly accounts for the presence of the bid/ask spread encountered in price-driven markets....

In the present paper we study the stability of a threshold continuos-time model that belongs to the class of Piecewise Deterministic Markov Processes. We derive a sufficient condition on the coefficients of the model to ensure the exponential ergodicity of the process under two different...