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lgianferrari
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Joined: September 17th, 2007, 12:26 pm

Ill-conditioned matrix for the CDO pricer

February 11th, 2008, 10:48 am

Dear everybody, I have a numerical question about an issue of the CDO pricer: I am applying the usual Andersen algorithm (the one that calculates deltas by inverting the matrix having (1-pk) in the diagonal and pk in one of the lower diagonals), where pk is the probability of default of issuer k.My question is: if spreads are very high (like now), and hence pk are very high, the matrix becomes ill-conditioned and almost cannot be inverted. Ideally, this happens when pk>0.5 (the whole stability depends from the parameter pk/(1-pk) ). Does anybody know how to bridge this problem?Let me know!!!Lo
 
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mikeoz
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Joined: September 28th, 2005, 2:58 pm

Ill-conditioned matrix for the CDO pricer

February 12th, 2008, 2:24 pm

When p>0.5, use the survival version of the tree instead of the default version, and use 1-p.