Dresden 2006 – wissenschaftliches Programm

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AKSOE: Physik sozio-ökonomischer Systeme

AKSOE 2: Financial Markets and Risk Management I

AKSOE 2.2: Vortrag

Montag, 27. März 2006, 10:45–11:15, BAR 205

The Multi-Fractal Model of Asset Returns: Its Estimation via GMM and its Use for Volatility Forecasting — •Thomas Lux — Department of Economics, University of Kiel, Olshausenstr. 40, 24118 Kiel

Multi-fractal processes have been proposed as a new formalism for modeling the time series of returns in finance. The major attraction of these processes is their ability to generate various degrees of long memory in different powers of returns - a feature that has been found to characterize virtually all financial prices. Furthermore, elementary variants of multi-fractal models are very parsimonious formalizations of the volatility dynamics as they essentially amount to one-parameter families of stochastic processes. The aim of this paper is to introduce a new and versatile estimation method for the causal multifractal of Calvet and Fisher (2001) and to use its parameter estimates in forecasting financial volatility. We use the auto-covariances of log increments of the multi-fractal process in order to estimate its parameters consistently via GMM (Generalized Method of Moment). Simulations show that this approach leads to essentially unbiased estimates, which also have much smaller root mean squared errors than those obtained from the traditional scaling approach. Our empirical estimates are used in out-of-sample forecasting of volatility for a number of important financial assets.