Measuring implied volatility: Is an average better? Which average?

Options researchers have argued that by averaging together implied standard deviations, or ISDs, calculated from several options with the same expiry but different strikes, the noise in individual ISDs can be reduced, yielding a better measure of the market's volatility expectation. Various options researchers have suggested different weighting schemes for calculating these averages. In the forecasting literature, econometricians have made the same argument but suggested quite different weighting schemes. Ignoring both literatures, commercial vendors calculate ISD averages using their own weightings. We compare the averages proposed in both the options and econometrics literatures and the averages used by major commercial vendors for the S&P 500 futures options market. Although some averages forecast better than others, we find that the question of the best weighting scheme is of secondary importance. More important is the fact that the ISDs are upward biased measures of expected volatility. Fortunately, this bias is stable over time, so past bias patterns can be used to obtain unbiased volatility forecasts. Once this is done, most ISD averages forecast better than time series and naive models, and the differences between the averages produced by the various proposed weighting schemes are small.