Valuation of Credit Contingent Options with Applications to Quanto CDS

We study the valuation of credit-contingent asset or options by modelling the correlation between asset price and credit default. We provide three ways of modelling 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. We show 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. We also obtain analytical solutions if default hazard rate, asset price return, and the copula are all Gaussian. Our experience shows that valuation is much more sensitive to the first and third type of correlations. We apply 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.