The Density of Distributions from the Bondesson Class

Abstract

In this paper, we derive an integral representation for the density of distributions from the Bondesson class, a large subclass of positive, infinitely divisible distributions. One striking advantage of this representation is its numerical stability: the oscillating integrand and the infinite integration bounds of the standard Bromwich Laplace inversion integral are circumvented, discretization errors are reduced and truncation errors are eliminated. This significantly enlarges the class of numerically tractable stochastic time transformations. Furthermore, we discuss the pricing of collateralized debt obligations for a large class of portfolio default models.

Keywords: Bernstein Function, Bondesson Class, Bromwich Inversion, Contour Transformation, Laplace Inversion, Lévy Subordinator