From various empirical work, it is well known that the volatility of asset returns changes over time. This might be one of the reasons that implied volatilities differ for options that only differ in time to maturity. We construct models for the relation between short- and long-term implied volatilities based on three different assumptions of stock return volatility behavior, i.e., mean-reverting, GARCH, and EGARCH models. We test these relations on option price data and conclude that EGARCH gives the best description of asset prices and the term structure of options' implied volatilities.

This paper proposes an extended market model for event studies based on daily stock returns. For actual data the assumptions of the simple market model are violated. The return distribution is not normal and neither the variance of the error term nor the risk parameter beta are constant. Our model incorporates the generalized autoregressive conditional heteroskedasticity (garch) model with t-distributed errors and a time-dependent beta. We test for anomalies by adding dummy variables in the regression equation. Our model is fairly general and could be used in a wide variety of event study situations. We illustrate the model by an analysis of the weekend and the option-expiration effect. We use return data from the Dutch stock market. The weekend effect on stock returns is significant, but no expiration effect could be detected.