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Positive Semi definite matrix and Cholesky
Hi everyone!I am probably going to ask a silly question but I used the Cholesky VBA code found in Wilmott on Quanitative finance and so far all the correlation matrix I have could be factorize. Does than mean that all my matrix are positive semi definite? Many thanks in advance!
Positive Semi definite matrix and Cholesky
You're dealing with correlation matrix, therefore...
Positive Semi definite matrix and Cholesky
Use the methods proposed by Peter Jackel (spectral sqaure root of symmetric matrix) rather than cholesky.
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- AlphaNumericus
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Positive Semi definite matrix and Cholesky
Suppose, for example, your matrix has the historical covariances of various spot fx rates (to USD). Suppose one of the currencies is tied to a basket of other currencies, i.e. its exchange rate is always the same linear combination of some other currencies' exchange rates to USD. Then it will give rise to a zero eigenvalue and Choleski will fail. Choleski needs positive definite matrices to work, while correlation matrices may be non-negative definite.