Hidden Regime-switching Models for Estimating Financial Volatility

Abstract

In this thesis, the behavior of the S&P 500 index is investigated in terms of its volatility. The main purpose is to derive a simple investment strategy that takes risk management into account. Based on data from the S&P 500 and the VIX index in the period between the 2nd of January 1990 to the 16th of October 2023, different kinds of Markov-switching models are used to estimate the volatility. These hidden regime-switching models contain GARCH, EGARCH, or GJR processes, respectively. In continuation of this work, the optimal number of regimes is studied through different model selection criteria like AIC, BIC, and DIC. The models are built via the MSGARCH package in R and they are based on either the maximum likelihood method or Markov Chain Monte Carlo simulations. Consequently, the thesis also makes a comparison of these methods, but it is limited to the relevant work of this paper. Usually, financial and economic time series are characterized by some stylized facts, such as asymmetries and the leverage effect. In this context, the CARCH process has a clear weakness since it does not distinguish between positive and negative returns. On the other hand, both EGARCH and GJR processes take this into account and they agree with each other to a large extent regarding the timing of the regime shifts, even though their estimated volatility is not identical. It seems like the GJR process adapts quicker to spikes in the volatility while the EGARCH process adapts quicker to low volatility. The thesis suggests that people should be in the market when the volatility is low. In other words, if the regime-switching model is based on EGARCH or GJR with only two regimes, the investor should follow the low-volatility regime. The VIX index can also work as an early warning for these regime shifts. In some cases, the regime shifts of the VIX index even indicate a better timing compared to the other models in terms of a rising S&P 500 index. In general, these models appear useful for risk-averse investors without a 30-year time frame.