Valuing Retail Credit Tranches with Structural, Double Mixture Models

This study considers the class of double mixtures to model a general dependence structure beyond the typical conditional independence assumption among the entities in a homogeneous credit portfolio. The two mixing components are (i) the marginal distributions of the systemic and idiosyncratic factors and (ii) the conditional probability measure that incorporates the further dependence structure among the idiosyncratic factors, given the systemic factor. For a large portfolio, the fair spread of a structured retail credit tranche is expressed in terms of the sums of single integrals, which can be easily computed numerically. We discuss the behaviors of tranche spreads under several double mixture models, and calibrate these models to market data. © 2015 Wiley Periodicals, Inc. Jrl Fut Mark 35:849–867, 2015