This is How You Make a GARCH Smile - An Improved Estimation and Calibration Method for a Family of GARCH Models

Abstract

This paper proposes an improved estimation and calibration method to a family of GARCH models. The suggested method fixes one parameter such that the unconditional kurtosis of the model matches the sample kurtosis. The method can be used to estimate the model on historical returns, or calibrate it on observed option prices. An empirical analysis using Engle and Ng's (1993) NGARCH(1,1) model shows that the method dominates previous estimation methods on multiple aspects. When estimating on historical returns, the processing time is cut in half, and the out of sample fit is improved. When calibrating on observed option prices, the optimization is simplified and the processing time is reduced by 50%, without affecting the quality of the fit. Results are robust to various samples and selection of initial values.

Keywords: NGARCH, Volatility, Kurtosis, Smile, Targeting

JEL Classification: G12, C12