Structural Breaks in GARCH Processes Do Matter

Abstract

Structural breaks in GARCH processes do matter for applications and model-based inference. To show this, I first propose a new approach to estimate change-point GARCH models with maximum likelihood, for which no method exists so far. Practical implementation of the proposed algorithm is discussed and its effectiveness and properties are demonstrated in simulation studies. Building on the new method, the paper shows empirically that the inclusion of structural breaks changes the results of typical model applications both qualitatively and quantitatively. First, I document that standard GARCH models systematically overpredict volatility in low volatility periods, and underpredict in high volatility times, while the change-point GARCH model is able to overcome this bias. Similarly, a GARCH option pricing model systemically overprices options in calm periods, and underprices in turbulent times. Finally, adding structural breaks to GARCH models with jumps drastically changes the inference on risk-premia as well as the intensity and occurrence of jumps.