Regensburg 2007 – scientific programme

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AKSOE: Arbeitskreis Physik sozio-ökonomischer Systeme

AKSOE 14: Financial Markets and Risk Management III

AKSOE 14.6: Talk

Thursday, March 29, 2007, 16:45–17:15, H8

Correlation matrices of synthetic continuous time random walks — •Daniel Fulger¹, Enrico Scalas², and Guido Germano¹ — ¹Philipps-University Marburg, 35032 Marburg, Germany — ²Amedeo Avogadro University of East Piedmont, 15100 Alessandria, Italy

We present a method for the simulation of anomalous diffusion processes governed by time and space fractional differential equations. Processes of this kind are used e.g. to model high-frequency financial time series. The method is based on Monte Carlo simulation of continuous time random walks with Mittag-Leffler distributed waiting times and Lévy distributed jumps. Our new combination of fast techniques for the generation of Mittag-Leffler and Lévy deviates outruns previous simulation methods by orders of magnitude. This enables to generate a great number of synthetic time series in a short time and thus to perform on a large scale a new kind of null-hypothesis tests within random matrix theory, that is a useful theory to analyze and de-noise time series employing empirical correlation matrices. The latter are also important in financial risk analysis.