Testing mean reversion in financial market volatility; Evidence from s&p 500 index futures

Abstract

This article presents a comprehensive study of continuous time GARCH (generalized autoregressive conditional heteroskedastic) modeling with the thin-tailed normal and the fat-tailed Student's-t and generalized error distributions (GED). The study measures the degree of mean reversion in financial market volatility based on the relationship between discrete-time GARCH and continuous-time diffusion models. The convergence results based on the aforementioned distribution functions are shown to have similar implications for testing mean reversion in stochastic volatility. Alternative models are compared in terms of their ability to capture mean-reverting behavior of futures market volatility. The empirical evidence obtained from the S&P 500 index futures indicates that the conditional variance, log-variance, and standard deviation of futures returns are pulled back to some long-run average level over time. The study also compares the performance of alternative GARCH models with normal, Student's-t, and GED density in terms of their power to predict one-day-ahead realized volatility of index futures returns and provides some implications for pricing futures options. © 2008 Wiley Periodicals, Inc.