The informational quality of implied volatility and the volatility risk premium

Abstract

This article examines the informational quality of implied volatility in forecasting future realized volatility using daily S&P 500 and S&P 100 index option prices from 2000 to 2006. In contrast to many previous studies, we find that implied volatility is an unbiased and efficient estimator of future realized volatility. Unlike implied volatility estimates; both historical and conditional volatility estimates using GARCH and EGARCH models possess limited explanatory power. A delta-hedged trading strategy with long positions in calls, however, generates significantly negative profits that imply a misspecification of constant volatility models. These results suggest that implied volatility estimates from constant volatility models contain valuable information, even though the model might be misspecified.

Notes

¹ Since 1993, the Chicago Board option Exchange has been releasing information on market wide volatility through a volatility index based on the S&P 500, namely the VIX. This index is updated minute by minute during each trading day. These calculations are based on the constant volatility model of Black–Scholes up until September 2003. After that date, the CBOE changed to a model-free procedure. They claim that ‘VIX has been considered by many to be the world's premier barometer of investor sentiment and market volatility’ (www.cboe.com).

² Fair and Shiller (1990) introduce the regression specification contained in Equation 3(3) which is generally referred as the ‘encompassing test’ in the forecasting literature.

³ SEs are based on the sample SD divided by square root of number of observations, following the method used by Bakshi and Kapadia (2003).