Valuation of credit contingent interest rate swap with credit rating migration

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.

本文提出一种适用于带有信用评级迁移的信用关联利率互换（Credit Contingent Interest Rate Swap，CCIRS）的灵活定价模型，该模型对随机利率与交易对手违约风险具有敏感性，此为一种全新的CCIRS定价模型。研究将基础利率互换（Interest Rate Swap，IRS）的交易对手划分为高、低两个信用等级，并首次基于结构化框架以利率为依托对信用评级迁移进行建模。此外，基础利率互换的违约事件采用简约式框架进行建模。通过分析CCIRS合约的现金流，本文推导得到带有信用评级迁移的CCIRS价值所满足的偏微分方程（Partial Differential Equation，PDE）。最后，本文讨论了采用交替方向隐式（Alternating Direction Implicit，ADI）方法求解得到的数值结果与参数分析，并给出了结合正则显式格式的数值算法的收敛速率。