I develop various frameworks for the separation of loss given default and default intensity present in securities with credit risk. They include spot and forward credit default swaps, digital default swaps and bonds. Cross-sectional no-arbitrage restriction between different securities extracts the pure measure of default intensity and loss given default not contaminated by the other. Using spo...

The correct modeling of default dependence is essential for the valuation of multiname credit derivatives. However for the pricing of synthetic CDOs a one-factor Gaussian copula model with constant and equal pairwise correlations, default intensities and recovery rates for all assets in the reference portfolio has become the standard market model. If this model were a reflection of market opini...

This paper describes a flexible and tractable bottom-up dynamic correlation modelling framework with a consistent stochastic recovery specification. In this modelling framework, only the joint distributions of default indicators are determined from the calibration to the index tranches; and the joint distribution of default time and spread dynamics can be changed independently from the CDO tran...

This paper presents a semi-analytical valuation method for basket credit derivatives in a flexible intensity-based model. Default intensities are modeled as correlated affine jump-diffusions. An empirical application documents that the model fits market prices of benchmark basket credit derivatives reasonably well, consistent with the observed correlation skew. Hence, I argue, contrary to comme...

This paper presents a simple reduce-form approach to pricing credit derivatives. The definition of default is purely based on the market value of a risky bond and its potential recovery value. A risky bond is treated as a riskless bond with an embedded short position on a barrier option. The risky bond market implicitly prices this barrier option. The default implied volatility (DIV) curve for ...

This paper employs non-parametric specification tests developed in Hong and Li (2005) to evaluate several one-factor reduced-form credit risk models for actual default intensities. Using estimates for actual default probabilities provided by Moody’s KMV from 1994 to 2005 for 106 U.S. firms in seven industry groups, we strongly reject popular univariate affine model specifications. As a good com...

This paper employs non-parametric specification tests developed in Hong and Li (2005) to evaluate several one-factor reduced-form credit risk models for actual default intensities. Using estimates for actual default probabilities provided by Moody’s KMV from 1994 to 2005 for 106 U.S. firms in seven industry groups, we strongly reject popular univariate affine model specifications. As a good com...

Common Failings: How Corporate Defaults are Correlated We develop, and apply to data on U.S. corporations from 1979-2004, tests of the standard doubly-stochastic assumption under which firms’ default times are correlated only as implied by the correlation of factors determining their default intensities. This assumption is violated in the presence of contagion or “frailty” (unobservable explana...

Evaluation of default correlation is an important task in credit risk analysis. In many practical situations, it concerns the joint defaults of several correlated firms, the task that is reducible to a first passage time (FPT) problem. This task represents a great challenge for jump-diffusion processes (JDP), where except for very basic cases, there are no analytical solutions for such problems...