Oct
24

## Nearest correlation matrix

Correlation matrix exists almost everywhere for derivative pricing and risk management, especially when Monte Carlo simulation is applied, for instance, to simulate correlated random numbers via Cholesky decomposition of correlation matrix. However, one strong requirement of Cholseky decomposition on correlation matrix is positive semi-definite, in other words, eigenvalues must be positive. Another example of positive semi-definite correlation matrix requirement is for risk management measurement, otherwise the volatility calculated might be negative, which is non-acceptable.

In practice, sometimes we need to change correlation matrix to our forecasting values, even minor change might lead to invalid matrix, for this problem, http://www.maths.manchester.ac.uk/~nareports/narep369.pdf details the way to overcome it, accompanying Matlab code can also be found at http://www.maths.manchester.ac.uk/~clucas/near_cor.m and http://www.maths.manchester.ac.uk/~clucas/eig_mex.c.

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In practice, sometimes we need to change correlation matrix to our forecasting values, even minor change might lead to invalid matrix, for this problem, http://www.maths.manchester.ac.uk/~nareports/narep369.pdf details the way to overcome it, accompanying Matlab code can also be found at http://www.maths.manchester.ac.uk/~clucas/near_cor.m and http://www.maths.manchester.ac.uk/~clucas/eig_mex.c.

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