Regensburg 2004 – scientific programme

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SYFT: Fat-Tail Distributions - Applications from Physics to Finance

SYFT 2: Fat-Tail Distributions - Applications from Physics to Finance

SYFT 2.4: Fachvortrag

Thursday, March 11, 2004, 12:45–13:00, H1

Robust estimation of correlation matrices and principal component analysis for fat-tailed elliptical distributions — •Uwe Jaekel¹ und Gabriel Frahm² — ¹NEC Europe Ltd., C&C Research Laboratories, Rathausallee 10, 53757 St. Augustin — ²Research Center CAESAR, Project Group Financial Engineering, Ludwig-Erhard-Allee 2, 53175 Bonn

Many problems in physics and finance require the estimation of covariance and correlation matrices. We present a maximum likelihood method for the estimation of these matrices that, unlike the commonly used moment estimator, is robust for the large class of elliptically contoured distributions, thus leading to substantially better estimates in the presence of fat tails. We try to reduce the complexity of the estimation problem using Bayes or Akaike information criteria, and compare this to attempts based on random matrix theory. The methods are applied to high-dimensional simulated and observed equity market data sets. Finally, we sketch some applications to the analysis of financial markets and to practical problems like portfolio risk minimisation.