Abstract
A model of O-U process with discrete noises is proposed for the price micro-movement, which refers to the transactional price behavior. The model can be viewed as a multivariate point process and framed as a filtering problem with counting process observations. Under this framework, the whole sample paths are observable and are used for parameter estimation. Based on the filtering equation, we construct a consistent recursive algorithm to compute the approximate posterior and the Bayes estimates. Finally, Bayes estimates for a two-month transaction prices of Microsoft are obtained.
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