Common well-known properties of time series of financial asset values include volatility clustering and asymmetric volatility phenomenon. Hidden Markov models (HMMs) have been proposed for modeling these characteristics, however, due to their simplicity, HMMs may lack two important features. We identify these features and propose modeling financial time series by recent Pairwise Markov models (PMMs) with a finite discrete state space. PMMs are extended versions of HMMs and allow a more flexible modeling. A real-world application example demonstrates substantial gains of PMMs compared to the HMM