Actuarial Applications of Multifractal Modeling Part II: Time Series Applications

Special Topics (narrow topic or advanced); Multifractals are mathematical generalizations of fractals, objects displaying "fractional dimension," "scale invariance," and "self-similarity.'" Many natural phenomena, including some of considerable interest to the casualty actuary (meteorological conditions, population distribution, financial time series), have been found to be well-represented by (random) multifractals. In part II of this paper, we show how to fit multifractal models in the context of one-dimensional time series. We also present original research on the multifractality of interest rate time series and the inadequacy of some state-of-the-art diffusion models in capturing that multifractality.