Lévy matrices and financial covariances

Zdzislaw Burda, Jerzy Jurkiewicz, Maciej A. Nowak, G. Papp, Ismail Zahed

Research output: Chapter in Book/Report/Conference proceedingChapter

7 Citations (Scopus)

Abstract

In a given market, financial covariances capture the intra-stock correlations and can be used to address statistically the bulk nature of the market as a complex system. We provide a statistical analysis of three SP500 covariances with evidence for raw tail distributions. We study the stability of these tails against reshuffling for the SP500 data and show that the covariance with the strongest tails is robust, with a spectral density in remarkable agreement with random Lévy matrix theory. We study the inverse participation ratio for the three covariances. The strong localization observed at both ends of the spectral density is analogous to the localization exhibited in the random Lévy matrix ensemble. We discuss two competitive mechanisms responsible for the occurrence of an extensive and delocalized eigenvalue at the edge of the spectrum: (a) the Lévy character of the entries of the correlation matrix and (b) a sort of off-diagonal order induced by underlying inter-stock correlations. (b) can be destroyed by reshuffling, while (a) cannot. We show that the stocks with the largest scattering are the least susceptible to correlations, and likely candidates for the localized states. We introduce a simple model for price fluctuations which captures behavior of the SP500 covariances. It may be of importance for assets diversification.

Original languageEnglish
Title of host publicationActa Physica Polonica B
Pages4747-4763
Number of pages17
Volume34
Edition10
Publication statusPublished - Oct 2003

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matrices
matrix theory
complex systems
entry
statistical analysis
eigenvalues
occurrences
scattering

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Burda, Z., Jurkiewicz, J., Nowak, M. A., Papp, G., & Zahed, I. (2003). Lévy matrices and financial covariances. In Acta Physica Polonica B (10 ed., Vol. 34, pp. 4747-4763)

Lévy matrices and financial covariances. / Burda, Zdzislaw; Jurkiewicz, Jerzy; Nowak, Maciej A.; Papp, G.; Zahed, Ismail.

Acta Physica Polonica B. Vol. 34 10. ed. 2003. p. 4747-4763.

Research output: Chapter in Book/Report/Conference proceedingChapter

Burda, Z, Jurkiewicz, J, Nowak, MA, Papp, G & Zahed, I 2003, Lévy matrices and financial covariances. in Acta Physica Polonica B. 10 edn, vol. 34, pp. 4747-4763.
Burda Z, Jurkiewicz J, Nowak MA, Papp G, Zahed I. Lévy matrices and financial covariances. In Acta Physica Polonica B. 10 ed. Vol. 34. 2003. p. 4747-4763
Burda, Zdzislaw ; Jurkiewicz, Jerzy ; Nowak, Maciej A. ; Papp, G. ; Zahed, Ismail. / Lévy matrices and financial covariances. Acta Physica Polonica B. Vol. 34 10. ed. 2003. pp. 4747-4763
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