Conditional Markov regime switching model applied to economic modelling

In this paper we discuss the calibration issues of regime switching models built on mean-reverting and local volatility processes combined with two Markov regime switch- ing processes. In fact, the volatility structure of this model depends on a first exogenous Markov chain whereas the drift structure depends on a conditional Markov chain with re- spect to the first one. The structure is also assumed to be Markovian and both structure and regime are unobserved. Regarding this construction, we extend the classical Expectation- Maximization (EM) algorithm to be applied to our regime switching model. We apply it to economic datas (Euro-Dollars foreign exchange rate and Brent oil price) to show that this modelling well identifies both mean reverting and volatility regimes switches. More- over, it allows us to give economic interpretations of this regime classification such as some financial crisis or some economic policies.