Long Memory Persistence in the Factor of Implied Volatility Dynamics

The volatility implied by observed market prices as a function of the strikeand time to maturity form an Implied Volatility Surface (IV S). Practicalapplications require reducing the dimension and characterize its dynamicsthrough a small number of factors. Such dimension reduction is summarizedby a Dynamic Semiparametric Factor Model (DSFM) that characterizes theIV S itself and their movements across time by a multivariate time series offactor loadings. This paper focuses on investigating long range dependencein the factor loadings series. Our result reveals that shocks to volatility persistfor a very long time, affecting significantly stock prices. For appropriaterepresentation of the series dynamics and the possibility of improved forecasting,we model the long memory in levels and absolute returns using theclass of fractional integrated volatility models that provide flexible structureto capture the slow decaying autocorrelation function reasonably well.