Connecting the top-down to the bottom-up: Pricing CDO under a Conditional Survival (CS) model

In this paper, we use exact simulation to price CDO under a new dynamic model, the conditional survival (CS) model, which provided excellent calibration to both iTraxx tranches and underlying single nameCDS spreads onMarch 14, 2008, the day before the collapse of Bear Sterns, when the market was highly volatile. The distinct features of the CS model include: (1) it is able to generate clustering of defaults occurring dynamically in time and strong cross-sectional correlation, i.e., the simultaneous defaults of many names, both of which have been evidenced in the current subprime mortgage crisis; (2) it incorporates idiosyncratic default risk of single names but does not specify concrete models for them; (3) it provides automatic calibration to underlying single name CDS; (4) it allows fast CDO tranche pricing and calculation of sensitivity of CDO tranches to underlying single name CDS.