Hidden Markov models for financial optimization problems

Abstract

Many financial decision problems require scenarios for multivariate financial time series that capture their sequentially changing behaviour, including their extreme movements. We consider modelling financial time series by hidden Markov models (HMMs), which are regime-switching-type models. Estimating the parameters of an HMM is a difficult task and the multivariate case can pose serious implementation issues. After the parameter estimation, the calibrated model can be used as a scenario generator to describe the future realizations of asset prices. The scenario generator is tested in a single-period mean–conditional value-at-risk optimization problem for portfolio selection.