Markov Switching in GARCH Processes and Mean-Reverting Stock-Market Volatility

Abstract

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 behavior 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 reverts to near-normal levels fairly quickly following a spike.

KEY WORDS:

• Asset-price volatility
• Conditional heteroscedasticity
• Kurtosis