We propose a reduced-form model for credit risk in a multivariate setting where the intensities of defaults are driven by affine jump diffusions processes. An important example of application for the model is a portfolio of bonds issued by many obligors, such as a Collateralized Debt Obligation (CDO). By modeling the intensities of defaults of each obligor, one can produce default scenarios that are necessary to simulate the cashflows of the collateral portfolio and hence to estimate the risk associated to any tranche of a CDO.
We assume that defaults may occur as a consequence of three independent types of credit events: the idiosyncratic one, depending only on the particular situation of the obligor, the sectoral one, affecting all the obligors belonging to a given group, the general one, affecting all the obligors. The intensities of the independent credit events are affine jump diffusion processes and the default intensity process of each obligor is a linear combination of them.