Free random Lévy variables and financial probabilities

Zdzisław Burda, Jerzy Jurkiewicz, Maciej A. Nowak, Gábor Papp and Ismail Zahed

Physica A: Statistical Mechanics and its Applications, 2001, vol. 299, issue 1, 181-187

Abstract: We suggest that Free Random Variables, represented here by large random matrices with spectral Lévy disorder, may be relevant for several problems related to the modeling of financial systems. In particular, we consider a financial covariance matrix composed of asymmetric and free random Lévy matrices. We derive an algebraic equation for the resolvent and solve it to extract the spectral density. The free eigenvalue spectrum is in remarkable agreement with the one obtained from the covariance matrix of the SP500 financial market.

Keywords: Lévy processes; Random matrix models; Financial analysis (search for similar items in EconPapers)
Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:299:y:2001:i:1:p:181-187

DOI: 10.1016/S0378-4371(01)00294-1

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