How Asymmetric Is U.S. Stock Market Volatility?

This paper explores the asymmetry that is the difference in the volatility response to positive and negative return shocks, in the volatility predictions of asymmetric time series models, implied volatility, and realized volatility. Both time series models and implied volatility predict an increase in volatility following large negative returns and ex post realized volatility normally rises as predicted. However, while asymmetric time series models, such as the EGARCH and GJR models, predict an increase in conditional volatility following a large positive surprise return (albeit a smaller increase than following a negative shock of the same magnitude), both implied volatility and realized volatility generally fall.