Long memory persistence in the factor of implied volatility dynamics. Preprint, Humboldt-University zu

Empirical studies show that the volatility implied by observed market prices as a func-tion of the strike price and time to maturity form an Implied volatility Surface (IV S), a high-dimensional object. For practical applications such as in risk management, it is desir-able to reduce the dimension of this object and characterize its dynamics through a small number of factors. Such dimension reduction may be summarized by a Dynamic Semipara-metric Factor Model (DSFM), that characterize the IVS itself and their movements across time by a multivariate time series of factor loadings. This paper focuses on the long range dependence in the levels, return and absolute returns of the time series of factor loadings obtain from the DSFM application on the German DAX index market. Fractal dynamics are detected in the loadings levels and absolute returns but no evidence in the returns. Fur-ther analysis is conducted by estimating the fractional parameter within the Autoregressive Fractional integrated moving average model (ARFIMA) frame work, as an information source that should be useful to regulators and derivative market participants to reasonably predict the stock market movements