Spot Variance Regressions

Abstract

We study a nonlinear vector regression model for discretely sampled high-frequency data with the latent spot variance of an asset as a covariate. We propose a two-stage inference procedure by first nonparametrically recovering the volatility path from asset returns and then conducting inference based on the generalized method of moments (GMM). The GMM estimator is nonstandard in that the second-order asymptotics is dominated by a bias term, rendering the standard inference implausible. We propose several bias-correction methods and show that the bias-corrected estimators have the parametric rate of convergence with mixture normal asymptotic distributions. We provide estimators for the asymptotic variance, as well as Anderson-Rubin-type confidence sets for the true parameter. Tests for overidentification and parameter stability are constructed. An empirical application on VIX pricing provides substantive evidence against conventional risk-neutral models for volatility dynamics.

Keywords: high frequency data, semimartingale, VIX, spot volatility, bias correction, GMM

JEL Classification: C22