具有随机波动率方差的信用等级迁移模型

A Credit Rating Migration Model with Stochastic Volatility Variance

摘要:

考虑到信用等级迁移带来的风险，通过债券定价方式，基于Heston模型建立了具有随机波动率方差的信用等级迁移模型，以此来评估信用风险。根据预先设定的资产阈值将公司债券分为高、低两个信用等级，公司资产的波动率方差在不同的信用等级下有不同的波动性，即波动率方差满足不同的CIR（cox-ingersoll-ross）过程。根据无套利原理等，推导出了高、低等级下债券价值满足的偏微分方程以及耦合边界处满足的条件。利用隐格式差分方法对债券价值求取数值解，并进行参数分析。

Abstract:

Based on the Heston model， a credit rating migration model with random volatility variance is established by means of bond pricing to evaluate credit risk. Corporation bonds are divided into high and low credit ratings based on predefined asset threshold.The volatility variance of corporate assets has different volatility at different credit ratings， i.e.， the volatility variance satisfies different CIR（cox-ingersoll-ross） processes. According to the no arbitrage principle， etc.， the partial differential equations is derived for bond values at high and low ratings and the conditions satisfied at the coupling boundary. Finally， the implicit scheme difference method is used to get the numerical solution of bond value.