Four-factor model of Quanto CDS with jumps-at-default and stochastic recovery

Abstract

We modify the model of Itkin, Shcherbakov and Veygman (ISV), proposed for pricing Quanto CDS and risky bonds, in several ways. First, the recovery rate could significantly vary right before or at default, therefore, here we treat it as stochastic. Second, we assume the domestic interest rate to be deterministic, because, as shown by ISV, its volatility does not contribute much to the Quanto CDS spread. Finally, to solve the corresponding systems of 4D PDEs we use a flavor of the RBF method which is a combination of localized RBF and finite-difference methods. Results of our numerical experiments demonstrate that the influence of volatility of the recovery rate is significant if the correlation between the recovery rate and the log-intensity of the default is non-zero. Also, the impact of the recovery mean-reversion rate on the Quanto CDS spread could be comparable with the impact due to jump-at-default in the FX rate.