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Free Lévy matrices and financial correlations

✍ Scribed by Zdzisław Burda; Jerzy Jurkiewicz; Maciej A. Nowak; Gabor Papp; Ismail Zahed

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
231 KB
Volume
343
Category
Article
ISSN
0378-4371

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✦ Synopsis

We consider a covariance matrix composed of asymmetric and free random LÃ evy matrices. We use the results of free random variables to derive an algebraic equation for the resolvent and solve it to extract the spectral density. For an appropriate choice of asymmetry and LÃ evy index =2 = 3 4 the free eigenvalue spectrum is in remarkable agreement with the one obtained from the covariance matrix of the SP500 ÿnancial market. Our results are of interest to a number of stochastic systems with power law noise.

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