Stochastic volatility with regime switching and uncertain noise: Filtering with sub-linear expectations

Abstract

This paper considers a new stochastic volatility model with regime switches and uncertain noise in discrete time and discusses its theoretical development for filtering and estimation. The model incorporates important features for asset price models, such as stochastic volatility, regime switches and parameter uncertainty in Gaussian noises for both the return and volatility processes. In particular, both drift and volatility uncertainties for the return and volatility processes are incorporated by introducing a family of real-world probability measures. Then, by modifying the reference probability approach to filtering, a sequence of conditional sub-linear expectations is used to provide a robust approach for describing the drift and volatility uncertainties in the Gaussian noises. Filtering theory, based on conditional sublinear expectations and the Viterbi algorithm are adopted to derive filters for the hidden Markov chain and filter-based estimates of the unknown parameters.