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

Zdzisław Burda, Andrzej Jarosz, Maciej Nowak, Jerzy Jurkiewicz, Gabor Papp and Ismail Zahed

Quantitative Finance, 2011, vol. 11, issue 7, 1103-1124

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.

Keywords: Portfolio theory; Power laws; Statistical physics; Risk measures; Random walks; Options pricing; Random matrix theory (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (6)

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DOI: 10.1080/14697688.2010.484025

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