Analysis of the Term Structure of Implied Volatilities

Abstract

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.