The benefits of returns and options in the estimation of GARCH models. A Heston-Nandi GARCH insight

Abstract

In a controlled, simulated setting, the questions of what the benefits are of including option prices in the estimation of GARCH models, the extent to which options can replace returns, and what the best type of options is for estimation, are addressed. The computational advantages of affine GARCH models for option pricing make these questions numerically tractable, therefore the experiments focus on the Heston-Nandi GARCH model. Three estimation methods, namely, returns-only estimation, options-only calibration and joint returns-options estimation-calibration are compared. The study reveals that, although the benefit is insignificant for the risk premium factor, adding options significantly reduces the standard errors of the GARCH dynamic parameters. This conclusion holds true under both linear and variance-dependent pricing kernels. The results suggest that, in a realistic setting, practitioners can use a large and recent sample of option prices to compensate for the lack of available return data. As a by-product, evidence also shows that out-of-the-money, short-maturity options are the best choice to improve the quality of the estimation.