A Gaussian Mixture Hidden Markov Model for the VIX

A Hidden Markov Model (HMM) is used to model the VIX (the Cboe Volatility Index). A 4- state Gaussian mixture is fitted to the VIX price history from 1990 to 2022. Using a growing window of training data, the price of the S&P500 is predicted and two trading algorithms are presented, based on the expected mean and standard deviation as well as the predicted state probabilities. The performance of these strategies is analyzed on the full data-set and compared to the results of a data-set of half the size. The strategies are compared to both a buy-n-hold strategy of the same period and the VXTH (the Cboe VIX Tail Hedge Index). The results presented here show promising application in modelling and predicting volatility, as well as identifying current volatility regimes predominating the market