Random matrix theory (RMT) in finance

The new kid on the block in finance seems to be random matrix theory. Although RMT as a theory is not so new (about 50 years) and was first used in quantum mechanics it being used in finance is a quite recent phenomenon.

RMT in itself is a fascinating area of study concerning the eigenvalues of random matrices and finding laws that govern their distribution (a little bit like the central limit theorem for random variables). These laws show up in all kinds of areas (even in such arcane places like the spacings of the zeros of the Riemann-Zeta function in number theory) - and nobody really understands why...

For a good first treatment see this non-technical article by Terence Tao.

My question:
Do you know (other) accessible intros to Random Matrix Theory - and its application in finance?

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Assume you've hit wikipedia? – barrycarter Feb 15 '11 at 15:30

Check out page 55 in "Quantitative Equity Investing: Techniques and Strategies," Fabozzi et al.

Section is titled "Random Matrix Theory" - very intro. The context pertains to the estimation of a large covariance matrix.

Also, see work at Capital Fund Management, filed under:

Random Matrix and Finance : correlations and portfolio optimisation

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Google for this paper "Financial applications of random matrix theory: Old laces and new piece" from Marc Potters, Jean-Philippe Bouchaud, and Laurent Laloux.

You can also check Prof. Gatheral presentation about Random Matrix Theory http://www.math.nyu.edu/fellows_fin_math/gatheral/RandomMatrixCovariance2008.pdf

In R, the package "tawny" has an implementation of RMT to filter noise in the correlation and covariance matrices.

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I'll throw this in as an "application of RMT" ... EDHEC and FTSE use RMT to decide the optimal number of principal components in their covariance estimation procedure for which they use PCA (Principal Component Analysis). For details look here or here in Appendix C section 4 for details.

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Beware that the assumptions usually made are not consistent with the practical applications, especially when heavy tails are considered. For the extension to a more realistic setting see this nice paper.

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