The valuation of multi-counterparties CDS with credit rating migration

Abstract

In this paper, the pricing of a Credit Default Swap (CDS) contract with multiple counterparties is considered. The pricing model takes into account the credit rating migration risk of the reference. It is a new model established under the reduced form framework, where the intensity rates are assumed to have structural styles. We derive from it a non-linear partial differential equation system where both positive and negative correlations of counterparties and the references are considered via a single factor model. Then, an ADI (Alternating Direction Implicit) difference method is used to solve the partial differential equations by iteration. From the numerical results, the comparison of multi-counterparty CDS contract and the standard one are analyzed respectively. Moreover, the impact of default parameters on value of the contracts are discussed.