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

Abstract

The pricing of collateralized debt obligations (CDOs) and other basket credit derivatives is contingent upon (i) a realistic modelling 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 modelling 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, including data in the midst of the 2008 financial credit crisis, and discuss the relative performance of the framework.

Key Words:

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

Acknowledgements

This work was partially supported by NSF grant DMS-0456195.