Multifractal Finance

Abstract

A striking feature of the prices of financial assets is that their statistical properties are to some degree universal across difierent assets, regions and epochs. There is a vast amount of literature on modelling these so-called stylized facts of financial data, but relatively recently multifractal processes have been proposed as a new formalism for financial modelling. Their main power lies in the fact that they capture many of the main statistical properties of financial time series in an effective way. The goal of this thesis is to present two multifractal models, the Multifractal Model of Asset Returns and the Markov-Switching Multifractal, and to study them in a more complete and rigorous way than in the literature.