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

TL;DR

This paper extends a model for pricing Quanto CDS by incorporating stochastic recovery rates and jumps-at-default, using a novel RBF-FD numerical method, revealing significant effects of recovery rate volatility and mean-reversion on spreads.

Contribution

It introduces a stochastic recovery rate into the four-factor Quanto CDS model and applies a new RBF-FD numerical method for solving the resulting PDEs.

Findings

Recovery rate volatility significantly impacts spreads when correlated with default intensity.

Mean-reversion rate of recovery influences spreads comparably to FX jumps.

The RBF-FD method effectively solves high-dimensional PDEs in this context.

Abstract

In this paper we modify the model of Itkin, Shcherbakov and Veygman, (2019) (ISV2019), proposed for pricing Quanto Credit Default Swaps (CDS) and risky bonds, in several ways. First, it is known since the Lehman Brothers bankruptcy that the recovery rate could significantly vary right before or at default, therefore, in this paper we consider it to be stochastic. Second, to reduce complexity of the model, we treat the domestic interest rate as deterministic, because, as shown in ISV2019, volatility of the domestic interest rate does not contribute much to the value of the Quanto CDS spread. Finally, to solve the corresponding systems of 4D partial differential equations we use a different flavor of the Radial Basis Function (RBF) method which is a combination of localized RBF and finite-difference methods, and is known in the literature as RBF-FD. Results of our numerical experiments presented in the paper 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.