Lehrstuhl für Geld, Währung und Internationale Finanzmärkte

Project Discription

The Multi-Fractal Model of Asset Returns: Multivariate Extensions, Estimation, and Applications for Risk Management

Multifractal processes have been originally developed in physics for modeling turbulent fluids and related phenomena. They have recently also attracted attention in empirical finance because of their ability to replicate the major stylized facts of asset returns: varying degrees of long-term correlation of different measures of volatility, and fat tails in the unconditional distribution of price changes. While the multifractal apparatus developed in statistical physics is mainly concerned with combinatorial operations on measures, analogous causal multifractal models have been designed for financial applications. Although this literature is still at a very early stage, it has already developed a range of statistical techniques for proper estimation of multifractal models and has demonstrated successful applications in forecasting of volatility. The present project builds upon the earlier work on inference methods for multifractal models and their practical applications by our group. One major task will be the development of appropriate statistical methodology for multivariate multifractal models. We will investigate the behavior of various extensions and explore the use of multifractal models for risk management and portfolio management. Further research includes the analysis of the role of innovations vis-à-vis the intrinsic volatility dynamics as well as the adaptation of the multifractal model to measures of realized volatility. Given the evidence on multi-scaling of many physical time series, we also expect that the methodological innovations in financial applications will generate spill over effects to the application of multifractal models in the natural science (for example, improved forecasts of precipitation).