In the present paper we apply the Gibbs Sampling approach to estimate the parameters of a MarkovSwitching Model which we use to model financial time series. In particular, we estimate the standard deviationof the time series in order to obtain an indicator similar to the VIX index. The Markov Switching technique hasbeen chosen because of the presence of exogenous factors which can have a large impact on the market, making itbehave differently in different time periods. We also perform a case study on the S&P500 index for the period 3January, 2007 - 29 December, 2014
