An Improved Estimation Method for a Family of GARCH Models

Abstract

This article 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. An empirical analysis using Engle and Ng’s (1993) NGARCH(1,1) model shows that the method dominates previous estimation methods in multiple ways. The optimization problem is simplified and made less sensitive to initial values. The optimization time, both when estimating based on historical returns and calibrating to option prices, is reduced by roughly 50%. The in-sample fit is barely affected, while the option pricing, both in sample and out of sample, is improved. TOPICS: Statistical methods, quantitative methods, options, derivatives