Analytical pricing of basket default swaps in a dynamic Hull-White framework

Frédéric D. Vrins

Abstract

ABSTRACT

In this paper, some analytical results related to the Hull-White dynamic model of a credit portfolio of N obligors with constant jump size are provided. This setup leads to analytical calibration of the model with respect to the underlying credit default swaps. Furthermore, extremely simple analytical expressions are obtained for first-to-default swaps. The more general case of quantities related to nth-to-default swaps also has a closed form and remains tractable for small n. In particular, the model leads to non-vanishing default correlation for shortterm maturities as opposed to the Gaussian copula approach. When calibrated to default probability of first default time, jump-based models also lead to much higher default probability for the last obligor to default. Finally, we tackle the problem of simultaneous jumps. To that end, we propose a tractable compromise to deal with baskets being non-homogeneous recovery-wise under the Hull-White model by splitting isolated and non-isolated default events.