Volatility analysis: a multifractional approach with mixtures of Beta distributions

Volatility estimation has become one of the core activities of financial analysts. At present, the majority of
buy and sell operations are run by “computer traders” that use algorithms mainly based on volatility levels in
the market. Several analyses argue that the recent “flash crash crisis” are the amplified consequence of
volatility variations. Among the various methodologies proposed in literature, fractals are playing a major role
in modeling financial series and, in particular, in analysing volatility characteristics. Following this line, we
propose a stochastic approach using a random variable to represent the Hurst Exponent H. We adopt an
iterative procedure to model H with a mixture of n Beta distributions, where the number of components will
depend on the required modeling accuracy. We choose several types of financial market indexes and assets
to evaluate the model and show that the proposed methodology can provide a deep insight into the volatility
characteristics associated to each one of them.