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This article presents a Markov chain framework to characterize the behavior of the CBOE Volatility Index (VIX index). Two possible regimes are considered: high volatility and low volatility. The specification accounts for deviations from normality and the existence of persistence in the evolution of the VIX index. Since the time evolution of the VIX index seems to indicate that its conditional variance is not constant over time, I consider two different versions of the model. In the first one, the variance of the index is a function of the volatility regime, whereas the second version includes an autoregressive conditional heteroskedasticity (ARCH) specification for the conditional variance of the index.
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VIX index Markov chain Realized volatility Implied volatility Volatility regimes