Volatility Puzzles: A Simple Framework for Gauging Return-Volatility Regression

34 Pages Posted: 18 Sep 2003

See all articles by Hao Zhou

Hao Zhou

Tsinghua University - PBC School of Finance

Tim Bollerslev

Duke University - Finance; Duke University - Department of Economics; National Bureau of Economic Research (NBER)

Date Written: March 2004

Abstract

This paper provides a simple theoretical framework for assessing the empirical linkages between returns and realized and implied volatilities. First, we show that whereas the volatility feedback effect as measured by the sign of the correlation between contemporaneous return and realized volatility depends importantly on the underlying structural model parameters, the correlation between return and implied volatility is unambiguously positive for all reasonable parameter configurations. Second, the asymmetric response of current volatility to lagged negative and positive returns, typically referred to as the leverage effect, is always stronger for implied than realized volatility. Third, implied volatilities generally provide downward biased forecasts of subsequent realized volatilities. Our results help explain previous findings reported in the extant empirical literature, and is further corroborated by new estimation results for a sample of monthly returns and implied and realized volatilities for the S\&P500 aggregate market index.

Keywords: Leverage Asymmetry, Volatility Feedback,Implied Volatility Forecast, Realized Volatility, Stochastic Volatility Model, Instrument Variable

JEL Classification: G12, G51, C22

Suggested Citation

Zhou, Hao and Bollerslev, Tim, Volatility Puzzles: A Simple Framework for Gauging Return-Volatility Regression (March 2004). FEDS Working Paper No. 2003-40. Available at SSRN: https://ssrn.com/abstract=445460 or http://dx.doi.org/10.2139/ssrn.445460

Hao Zhou (Contact Author)

Tsinghua University - PBC School of Finance ( email )

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Beijing, 100083
China
86-10-62790655 (Phone)

Tim Bollerslev

Duke University - Finance ( email )

Durham, NC 27708-0120
United States
919-660-1846 (Phone)
919-684-8974 (Fax)

Duke University - Department of Economics

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Box 90097
Durham, NC 27708-0204
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National Bureau of Economic Research (NBER)

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