Markov switching in GARCH processes and mean-reverting stock-market volatility

This article introduces four models of conditional heteroscedasticity that contain Markov-switching parameters to examine their multiperiod stock-market volatility forecasts as predictions of options-implied volatilities. The volatility model that best predicts the behaviour of the options-implied volatilities allows the Student-t degrees-of-freedom parameter to switch such that the conditional variance and kurtosis are subject to discrete shifts. The half-life of the most leptokurtic state is estimated to be a week, so expected market volatility to near-normal levels fairly quickly following a spike.