Applying free random variables to random matrix analysis of financial data. Part I: The Gaussian case

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

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

We apply the concept of free random variables to doubly correlated (Gaussian) Wishart random matrix models, appearing, for example, in a multivariate analysis of financial time series, and displaying both inter-asset cross-covariances and temporal auto-covariances. We give a comprehensive introduction to the rich financial reality behind such models. We explain in an elementary way the main techniques of free random variables calculus, with a view to promoting them in the quantitative finance community. We apply our findings to tackle several financially relevant problems, such as a universe of assets displaying exponentially decaying temporal covariances, or the exponentially weighted moving average, both with an arbitrary structure of cross-covariances.

Original languageEnglish
Pages (from-to)1103-1124
Number of pages22
JournalQuantitative Finance
Volume11
Issue number7
DOIs
Publication statusPublished - Jul 2011

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Financial data
Random variables
Assets
Quantitative finance
Exponentially weighted moving average
Multivariate analysis
Financial time series

Keywords

  • Options pricing
  • Portfolio theory
  • Power laws
  • Random matrix theory
  • Random walks
  • Risk measures
  • Statistical physics

ASJC Scopus subject areas

  • Economics, Econometrics and Finance(all)
  • Finance

Cite this

Applying free random variables to random matrix analysis of financial data. Part I : The Gaussian case. / Burda, Zdzislaw; Jarosz, Andrzej; Nowak, Maciej A.; Jurkiewicz, Jerzy; Papp, G.; Zahed, Ismail.

In: Quantitative Finance, Vol. 11, No. 7, 07.2011, p. 1103-1124.

Research output: Contribution to journalArticle

Burda, Zdzislaw ; Jarosz, Andrzej ; Nowak, Maciej A. ; Jurkiewicz, Jerzy ; Papp, G. ; Zahed, Ismail. / Applying free random variables to random matrix analysis of financial data. Part I : The Gaussian case. In: Quantitative Finance. 2011 ; Vol. 11, No. 7. pp. 1103-1124.
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