Forecasting stock-return variance: toward an understanding of stochastic implied volatilities

We examine the behavior of measured variances from the optionsmarket and the underlying stock market. Under the joint hypothesesthat markets are informationally efficient and that option pricesare explained by a particular asset pricing model, forecastsfrom time-series models of the stock return process should nothave predictive content given the market forecast as embodiedin option prices. Both in-sample and out-of-sample tests suggestthat this hypothesis can be rejected. Using simulations, weshow that biases inherent in the procedure we use to imply variancescannot explain this result. Thus, we provide evidence inconsistentwith the orthogonality restrictions of option pricing modelsthat assume that variance risk is unpriced. These results alsohave implications for optimum variance forecast rules.