This paper studies the valuation of credit contingent asset or options by modeling the correlation between asset price and credit default. It provides three ways of modeling such correlation: (1) asset value follows a diffusion process with a one-time jump (such as currency devaluation) at the time of credit default; (2) Default intensity and asset price are driven by correlated Brownian motions in addition to the jump; (3) Default time and future asset price are correlated through a copula. When both asset price and credit default are independent of interest rates, such contract can be valued on a two-dimensional lattice (or finite-difference grid) in the second approach. The paper shows that for a large class of one-factor default rate models, the computation can be reduced to one-dimension, a property often reserved for the affine class of models. It also obtains analytical solutions if default hazard rate, asset price return, and the copula are all Gaussian. Experience shows that valuation is much more sensitive to the first and third type of correlations. The paper applies the model to the valuation of extinguishable FX swaps that terminate upon a credit event and quanto credit default swaps, where premium and protection legs are paid in different currencies.

In general, valuation of credit contingent derivatives requires three factor models, one for interest rate, another for credit default, and the third for asset price. Even when interest rate is uncorrelated with both credit default and asset price process, a two factor model is still needed. Except in some special cases where analytical solution is available, such models are not practical to implement. We show that for a large class of asset price processes, the valuation problem reduces to the computation of survival probabilities in a one-factor diffusion model for the default intensity. This class goes much beyond the Affine Jump Diffusion (AJD) framework in Ehlers and Schonbucher (2006).

This framework is still problematic in practice due to difficulties in parameter estimation. The model requires at least three parameters related to the default rate volatility: asset price, default rate correlation and jump size (devaluation), respectively. On the other hand, the market often prefers a parsimonious model with a single number for correlation.2 To this end, we can model the joint distribution of default time (or equivalently the default event) and asset price through a copula. An analytical solution is available under the Gaussian copula. Numerical examples show that as we vary the correlation in the copula approach a very range of valuations can be obtained for the credit contingent derivatives contracts.

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