Ill-conditioned matrix for the CDO pricer
Posted: 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