Valuation of credit contingent interest rate swap with credit rating migration

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.

KEYWORDS:

• Credit contingent interest rates swap
• credit rating migration
• counterparty default risk
• credit risk measure
• derivative pricing model

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 91B30
• 65M06

Acknowledgments

We thank International Science Editing ( http://www.internationalscienceediting.com) for editing this manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Hongchun Zou  http://orcid.org/0000-0001-5744-1374

Additional information

Funding

This work was supported by National Natural Science Foundation of China [grant number 11671301].