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

Abstract

This paper introduces four models of conditional heteroscedasticity that contain markov switching parameters to examine their multi-period stock-market volatility forecasts as predictions of options-implied volatilities. The volatility model that best predicts the behavior of the optionsimplied 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 weak, so expected market volatility reverts to near-normal levels fairly quickly following a spike.

DEoptim: AnRPackage for Global Optimization by Differential Evolution

“…The interesting feature of these models lies in the fact that they provide an explanation of the high persistence in volatility, i.e., nearly unit root process for the conditional variance, observed with single-regime GARCH models (Lamoureux and Lastrapes 1990). Furthermore, these models are apt to react quickly to changes in the volatility level (unconditional volatility) which leads to significant improvements in volatility forecasts as shown by Dueker (1997) or Klaassen (2002) for instance. These features make the models attractive for various applications in financial modeling, such as risk management.…”

Détection non paramétrique de sauts dans la volatilité des marchés financiers

“…Parmi ces travaux, on retrouve ceux de Lamoureux et Lastrapes (1990), Hamilton et Susmel (1994), Cai (1994), Dueker (1997) et Maheu et McCurdy (2000). L'avantage de ces modèles relativement aux modèles GARCH standards est qu'ils permettent un ajustement très rapide à des périodes de haute ou basse volatilité.…”

Autoregressive Conditional Heteroscedasticity (ARCH) Models: A Review

“…The idea is, thus, to model changes in regime as changes in the scale of the process. Dueker [104] and Hansen [161] extended the approach to GARCH models.…”