Examining realized volatility regimes under a threshold stochastic volatility model

ABSTRACT This paper examines the realized volatility regimes under a threshold stochastic volatility (SV) model framework. Due to the availability of the volatility proxy, the estimation of the models' parameters can be easily implemented via standard maximum likelihood estimation (MLE) rather than using simulated Bayesian methods. In addition, the proposed model accommodates state‐dependent correlations between the return and volatility processes. This new feature can not only explain the so‐called leverage effect under the threshold SV framework, but also increase the flexibility of the model structure. Several mis‐specification and sensitivity experiments are conducted using Monte Carlo methods. In the empirical study, we apply the threshold SV structure to three stock indices. The results show that in different regimes, the returns and volatilities exhibit asymmetric behavior. In addition, this paper allows the threshold in the model to be flexible (or data driven) and uses a sequential optimization based on MLE to search for the ‘optimal'threshold value. We find that the model with a flexible threshold is always preferred to the traditional model with a fixed threshold according to the standard log‐likelihood measure. Interestingly, the ‘optimal’ threshold is found to be stable across different sampling realized volatility measures. Copyright © 2012 John Wiley & Sons, Ltd.