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

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Author Info

  • Zdzisław Burda
  • Andrzej Jarosz
  • Maciej Nowak
  • Jerzy Jurkiewicz
  • Gabor Papp
  • Ismail Zahed
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    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.

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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Quantitative Finance.

    Volume (Year): 11 (2011)
    Issue (Month): 7 ()
    Pages: 1103-1124

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    Handle: RePEc:taf:quantf:v:11:y:2011:i:7:p:1103-1124

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    Related research

    Keywords: Portfolio theory; Power laws; Statistical physics; Risk measures; Random walks; Options pricing; Random matrix theory;

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    Cited by:
    1. Stephan Süss, 2012. "The pricing of idiosyncratic risk: evidence from the implied volatility distribution," Financial Markets and Portfolio Management, Springer, vol. 26(2), pages 247-267, June.
    2. Collins, Benoît & Matsumoto, Sho & Saad, Nadia, 2014. "Integration of invariant matrices and moments of inverses of Ginibre and Wishart matrices," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 1-13.
    3. Desislava Chetalova & Rudi Sch\"afer & Thomas Guhr, 2014. "Zooming into market states," Papers 1406.5386, arXiv.org.

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