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

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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 Ding et al., 2008, 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 Fouque et al., 2003 and obtain explicit perturbation approximations to the loss distribution. We demonstrate the competence of our approach by calibrating it to the CDX index data.