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 switching 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 respect 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 ExpectationMaximization (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. Moreover, it allows us to give economic interpretations of this regime classification such as some financial crisis or some economic policies.