Loss Distributions of Credit Portfolios Containing Tranches and Repeated Obligors
13 Pages Posted: 21 Jul 2019 Last revised: 26 Feb 2020
Date Written: July 19, 2019
Semi-analytical methods are presented for computing joint loss distributions of credit portfolios in which obligors may occur more than once. A single-factor Gaussian copula model is used. It is demonstrated how to compute loss distributions if (1) some portfolio positions are tranches, (2) varying seniority bonds of the same obligor are present, and (3) obligors may be repeated across positions. The algorithm makes use of an exhaustive enumeration of scenarios and is exponential in time complexity. However, it is demonstrated that certain groups of conditional loss distributions can be combined using convolution which is faster than enumeration of scenarios. Monte Carlo simulations confirm the correctness of the proposed set of algorithms. The loss distribution of a portfolio of ten 10-name tranches with high overlap of names between tranches can be computed in approximately five seconds.
Keywords: joint loss distributions, single-factor Gaussian copula, repeated obligors, tranches
JEL Classification: G12
Suggested Citation: Suggested Citation