Multi-Scale Time-Changed Birth Processes for Pricing Multi-Name Credit Derivatives

Abstract

We develop two parsimonious models for pricing multi-name credit derivatives. We derive closed form expression for the loss distribution, which then can be used in determining the prices of tranche and index swaps and more exotic derivatives on these contracts. Our starting point is the model of [3], which takes the loss process as a time changed birth process. We introduce stochastic parameter variations into the intensity of the loss process and use the multi-time scale approach of [6] and obtain explicit perturbation approximations to the loss distribution. We demonstrate the competence of our approach by calibrating it to the CDX index data.

Keywords: Pricing multiname credit derivatives, pertubation approximation, multiple time scales, time changed birth processes, index/tranche swap, calibration