Multiscale Intensity Models and Name Grouping for Valuation of Multi-Name Credit Derivatives

Abstract

The pricing of collateralized debt obligations and other basket credit derivatives is contingent upon (i) a realistic modeling of the firms' default times and the correlation between them, and (ii) efficient computational methods for computing the portfolio loss distribution from the individual firms' default time distributions. Factor models, a widely-used class of pricing models, are computationally tractable despite the large dimension of the pricing problem, thus satisfying issue (ii), but to have any hope of calibrating CDO data, numerically intense versions of these models are required. We revisit the intensity-based modeling setup for basket credit derivatives and, with the aforementioned issues in mind, we propose improvements (a) via incorporating fast mean-reverting stochastic volatility in the default intensity processes, and (b) by considering homogeneous groups within the original set of firms. This can be thought of as a hybrid of top-down and bottom-up approaches. We present a calibration example, and discuss the relative performance of the framework.

Keywords: Collateralized debt obligations, intensity-based model, stochastic volatility, asymptotic approximation, multiple time scales, homogeneous-group factor models, bottom-up, top-down

JEL Classification: G12, G13