The implied volatility bias and option smile: is there a simple explanation?

Over the past 30 years, numerous option valuation models have been proposed hoping to explain the volatility smile and the volatility bias shown in the data. However, the Black and Scholes model remains the cornerstone of the option valuation model and its implied volatilities remain essential for calibrating parameters of the other option-valuation models. This research is the first in the literature to use a partial equilibrium model to explain the implied volatility bias using demand for and supply of the options market. The proposed theoretical model allows us to explain the existence of an upward bias and its determinants, and to simultaneously explain both the volatility smile and the volatility term structure. With data spanning the period of 1990 to 2008, twenty-six options on commodity futures markets are analyzed. For at-the-money options, as predicted by the proposed model, the implied volatility is found to be an upward-biased estimator of the realized volatility in nineteen markets. The implied volatility appears to be an unbiased estimator for the realized volatility in the cotton, oats, wheat No. 2, cocoa, orange juice, and heating oil markets. However, for out-of-the-money and in-of-the-money options, implied volatility appears to be an upward-biased estimator of the realized volatility. The theoretical model further suggests that the implied volatility's bias is caused by the quantity hedged, the strike, volatility, futures price, the risk-free rate, option prices, and days to maturity. The bias is different across strikes, times to maturity, puts and calls, option year, and exchanges. In most markets, the open interest and the historical return variables do not appear to have much impact. However, the historical volatility, the Risk free rate, and the Option price variables are shown to have a positive impact on the bias in most markets. The empirical model appears to explain the bias reasonably well with 30%-40% R2 in eleven markets and more than 50% R2 in thirteen markets. The results suggest that one should subtract the average bias presented here from the actual option premium before obtaining the implied volatility of the options. This could provide implied volatility which is a more accurate predictor of the future realized volatility.