Spot Variance Regressions

35 Pages Posted: 12 Feb 2013

See all articles by Jia Li

Jia Li

Duke University

Dacheng Xiu

University of Chicago - Booth School of Business

Date Written: February 10, 2013


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

Suggested Citation

Li, Jia and Xiu, Dacheng, Spot Variance Regressions (February 10, 2013). Chicago Booth Research Paper No. 13-07. Available at SSRN: or

Jia Li

Duke University ( email )

100 Fuqua Drive
Durham, NC 27708-0204
United States

Dacheng Xiu (Contact Author)

University of Chicago - Booth School of Business ( email )

5807 S. Woodlawn Avenue
Chicago, IL 60637
United States

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