Multifractal Volatility: Theory, Forecasting, and Pricing
Calvet and Fisher present a powerful, new technique forvolatility forecasting that draws on insights from the use ofmultifractals in the natural sciences and mathematics and providesa unified treatment of the use of multifractal techniques infinance. A large existing literature (e.g., Engle, 1982; Rossi,1995) models volatility as an average of past shocks, possibly witha noise component.This approach often has difficulty capturing sharpdiscontinuities and large changes in financial volatility. Theirresearch has shown the advantages of modelling volatility assubject to abrupt regime changes of heterogeneous durations. Usingthe intuition that some economic phenomena are long-lasting whileothers are more transient, they permit regimes to have varyingdegrees of persistence. By drawing on insights from the use ofmultifractals in the natural sciences and mathematics, they showhow to construct high-dimensional regime-switching models that areeasy to estimate, and substantially outperform some of the besttraditional forecasting models such as GARCH.The goal of Multifractal Volatility is to popularizethe approach by presenting these exciting new developments to awider audience. They emphasize both theoretical and empiricalapplications, beginning with a style that is easily accessible andintuitive in early chapters, and extending to the most rigorouscontinuous-time and equilibrium pricing formulations in finalchapters.