Abstract: We consider a risky asset whose price process follows a log-normal model with stochastic volatility. The volatility evolves according to a finite state Markov chain. The original observation process is this price process. We transform the process by introducing small noise so that the usual hidden Markov filtering techniques can be applied. The small noise coefficient is estimated by the quadratic variation technique. We consider the Zakai form of various related filtering processes which play important roles in the expectation maximization (EM) estimation of the transition intensities of the Markov chain. We consider a robust form of the filtering processes so that no stochastic integral appears in the equations.

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