Valuation of credit contingent interest rate swap with credit rating migration

Abstract

ABSTRACT In this paper, a flexible pricing model for Credit Contingent Interest Rate Swap (CCIRS) with credit rating migration is proposed, which is sensitive to stochastic interest rates and counterparty default risk. This is a new pricing model for CCIRS. The counterparty of the underlying interest rate swap (IRS) is considered to have a high and a low credit grade, and credit rating migration is modelled by the first attempt of the interest rate based on the structural framework. Furthermore, the default event for the underlying IRS is modelled using the reduced-form framework. The partial differential equation (PDE) satisfied by the value of CCIRS with credit rating migration is derived by analysing the cash flow of a CCIRS contract. Finally, the numerical results and parameter analysis, which are solved by using the alternating direction implicit (ADI) method, are discussed and the convergence rate of the numerical algorithm combined with a regular explicit scheme is also suggested.