担保信用等级变换的利率互换衍生品定价

Pricing of Interest Rate Swap Derivatives for Assuring Credit Rating Migration

摘要:

考虑担保信用等级迁移风险的利率互换合约, 在结构化方法的框架下，建立了担保信用等级首次迁移所造成损失的保费定价模型，信用等级依赖于利率并具有高低2个等级. 从一个新的角度将低等级下零息票利率互换的价值定义为保费价值的自变量，并利用对冲原理建立保费定价的偏微分方程模型. 利用计价单位转换原理对方程进行降维，求出问题的半解析解，然后采用有限差分方法的显式格式对模型进行数值求解. 最后,讨论了保费价值关于利率参数的依赖关系.结果表明:保费价值和各参数间存在单调递减的关系.

关键词:利率互换; 信用等级变换; 降维; 有限差分方法

Abstract:

Considering the valuation of a protected swap on credit rating migration, under the framework of structural methods, a pricing model was established for protecting the loss caused by the first credit rating migration, where the credit ratings depend on the interest rate and have two grades. In the pricing model, an independent variable of the model was defined by the value of lowgrade zerocoupon, which is a new perspective. A partial differential equation(PDE) pricing model was derived by the hedging method. A semiclosed solution was obtained by dimensionality reduction technique. The numerical solution was calculated by the explicit finite difference method. Finally, the dependency of parameters of the model was discussed and the results show that there is a monotonically decreasing relationship between premium value and each parameter.

Key words:interest rate swap; credit rating migration; dimensionality reduction; finite difference method