Bayesian Model Selection via Filtering for a Class of Micro-movement Models of Asset Price

This paper develops the Bayesian model selection based on Bayes factor for a rich class of partially-observed micro-movement models of asset price. We focus on one recursive algorithm to calculate the Bayes factors, first deriving the system of SDEs for them and then applying the Markov chain approximation method to yield a recursive algorithm. We prove the consistency (or robustness) of the recursive algorithm. To illustrate the construction of such a recursive algorithm, we consider a model selection problem for two micro-movement models with and without stochastic volaltility, and provide simulation and real-data examples to demonstrate the effectiveness of the Bayes factor in the model selection for this class of models.