Abstract: 
This paper explores differences in the impact of equally large positive and negative surprise return shocks in the aggregate U.S. stock market on: 1) the volatility predictions of asymmetric time series models, 2) implied volatility, and 3) realized volatility. Both asymmetric time series models and implied volatility predict an increase in volatility following large negative surprise 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 volatility following a large positive return shocks (albeit a much smaller increase than following a negative shock of the same magnitude), both implied and realized volatility generally fall sharply. While asymmetric time-series models predict a decline in volatility following near-zero returns, both implied and realized volatility are normally little changed from levels observed prior to the stable market. Reasons for the differences are explored.

Source: Ederington, Louis H. and Guan, Wei, How Asymmetric is U.S. Stock Market Volatility? (January 30, 2009). Available at SSRN: http://ssrn.com/abstract=1406175 or http://dx.doi.org/10.2139/ssrn.1406175