A multiple regime extension to the Heston–Nandi GARCH(1,1) model

In this article a multiple regime extension of a Heston–Nandi GARCH(1,1) class of models is presented to describe the asymmetries and intermittent dynamics in financial volatility. The statistical properties and the estimation of their parameters are addressed in detail. The number of regimes in the model is determined through a statistical procedure based on a robust Lagrange Multiplier (LM) specification. The ability of the model to forecast financial market volatility is empirically compared to standard GARCH models for a set comprising some of the major world stock indexes and their corresponding foreign exchange rates. A simulation-based analysis suggests the model is also able to approximate long memory behavior in volatility. A multiple regime extension of the base Heston–Nandi model is developed to price European style options using the filtered historical simulation framework. An empirical comparison against the base Heston–Nandi model is presented for S&P500 options at the height of the subprime crisis. It is demonstrated that the two regime extension provides a superior fit both in and out of sample.