A generalized partially linear model of asymmetric volatility

In this paper we conduct a close examination of the relationship between return shocks and conditional volatility. We do so in a framework where the impact of return shocks on conditional volatility is specified as a general function and estimated nonparametrically using implied volatility data—the Market Volatility Index (VIX). This setup can provide a good description of the impact of return shocks on conditional volatility, and it appears that the news impact curves implied by the VIX data are useful in selecting ARCH specifications at the weekly frequency. We find that the Exponential ARCH model of Nelson [Econometrica 59 (1991) 347] is capable of capturing most of the asymmetric effect, when return shocks are relatively small. For large negative shocks, our nonparametric function points to larger increases in conditional volatility than those predicted by a standard EGARCH. Our empirical analysis further demonstrates that an EGARCH model with separate coefficients for large and small negative shocks is better able to capture the asymmetric effect. D 2002 Elsevier Science B.V. All rights reserved. JEL classification: G10; C14