SeminarsRecursive Structure in Default Probabilities
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The probability distribution of the number of defaults in a group of entities plays an important role in multiple name pricing problems. When the group size becomes large, it is increasingly difficult to obtain its whole distribution. In this talk, we derive the recursive structure in these default probabilities based on Huge's formula for basket CDS prices. The recursive formula is useful for the calculation of the whole distribution and especially feasible when homogeneity is assumed. In order to allow inhomogeneity, the formula is further developed for a more general case where there are multiple subgroups of homogeneous entities. Through the numerical examples for a class of Markov chain based reduced-form models, we validate the proposed formulae with some discussions on computation time and accuracy including the effect of propagation error.
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Wei-Chung Mou
2009-06-10
10:20:00 - 12:00:00
405 , Mathematics Research Center Building (ori. New Math. Bldg.)
The probability distribution of the number of defaults in a group of entities plays an important role in multiple name pricing problems. When the group size becomes large, it is increasingly difficult to obtain its whole distribution. In this talk, we derive the recursive structure in these default probabilities based on Huge's formula for basket CDS prices. The recursive formula is useful for the calculation of the whole distribution and especially feasible when homogeneity is assumed. In order to allow inhomogeneity, the formula is further developed for a more general case where there are multiple subgroups of homogeneous entities. Through the numerical examples for a class of Markov chain based reduced-form models, we validate the proposed formulae with some discussions on computation time and accuracy including the effect of propagation error.