The Normal Inverse Gaussian Distribution for Synthetic CDO Pricing

Abstract

One of the harder new derivatives problems in recent years is estimating the probability distribution of credit losses on a portfolio of risky bonds or credit default swaps. This is the essential valuation problem for securitized debt instruments, including CDOs, CLOs, and CBOs, as well as exotic derivative contracts like „nth to default” swaps. The standard Gaussian copula model is not entirely satisfactory because it constrains correlation in the tails of the distribution in such a way that it is typically very hard to calibrate it to market tranche prices. The Student t-distribution has more plausible tail behavior, but because it is not stable under convolution, it becomes computationally very unwieldy as the number of variables increases. This article proposes the Normal Inverse Gaussian (NIG) distribution as a more tractable alternative. Comparison tests on several standard CDS index portfolios show that the NIG distribution has better tail characteristics than the Normal and it is much more efficient for large scale computations than the multivariate Student t.