Bayes estimation via filtering for a simple micro-movement model of asset price with discrete noises

Abstract

A simple partially observed model for micro-movement of stock prices is proposed. The micro-movement refers to the transactional price behavior. The model can be framed as a filtering problem with counting process observations. Under this framework, the whole sample path is observable and is used for parameter estimation. Based on the filtering equation, we construct a recursive algorithm to compute the approximate posterior and the Bayes estimates. The consistencies of the recursive algorithm and of Bayes estimates are proven. Bayes estimates for transaction prices of Microsoft are obtained with a financial application.