Multifractal Models : Estimation, Forecasting and Option Pricing
This thesis consists of studies in the field of multifractal models applied to financial time series. The first chapter provides a short introduction to the multifractal literature, preparing the terrain for the following chapters. Chapter 2 investigates new estimation and forecasting tools for the well-known multiplicative Lognormal cascade process. Chapter 3 presents a study on the identification and estimation of the Markov Switching Multifractal (MSM) model with finitely many levels in continuous time. Chapter 4 introduces a new way to obtain parameter estimates for a discrete-time MSM process through calibration to option price data. It focuses thereafter on the generation and evaluation of forecasts based on the historical as well as on the option-price time series. Appendix A provides additional results for the estimation procedures presented in Chapter 2. Appendix B goes into the details of the suggested future line of work with MSM models.