Modeling and pricing long memory in stock market volatility

A new class of fractionally integrated GARCH and EGARCH models for characterizing financial market volatility is discussed. Monte Carlo simulations illustrate the reliability of quasi maximum likelihood estimation methods, standard model selection criteria, and residual-based portmanteau diagnostic tests in this context. New empirical evidence suggests that the apparent long-run dependence in U.S. stock market volatility is best described by a mean-reverting fractionally integrated process, so that a shock to the optimal forecast of the future conditional variance dissipate at a slow hyperbolic rate. The asset pricing implications of this finding is illustrated via the implementation of various option pricing formula.