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### 资产波动率为随机的信用等级迁移风险评估模型

1. 同济大学数学科学学院, 上海 200092
• 收稿日期:2021-06-29 修回日期:2021-09-14 出版日期:2022-02-25 发布日期:2022-03-21
• 基金资助:
国家自然科学基金（12071349）资助课题.

LIANG Jin, ZHOU Huihui. An Evaluation Model of Credit Rating Migration Risk with Stochastic Asset Volatility[J]. Journal of Systems Science and Mathematical Sciences, 2022, 42(2): 304-317.

### An Evaluation Model of Credit Rating Migration Risk with Stochastic Asset Volatility

LIANG Jin, ZHOU Huihui

1. School of Mathematical Sciences, Tongji University, Shanghai 200092
• Received:2021-06-29 Revised:2021-09-14 Online:2022-02-25 Published:2022-03-21

In this paper, we use corporate bonds as a means to assess the risk of credit rating migration with random volatility. Different from the previous model for evaluating credit rating migration, this paper for the first time considers the risk of migration with random volatility. According to the size of the company's assets, the company is divided into high or low credit rating. It's assumed that the motion of the company's assets meets the Heston stochastic volatility model, and the volatility of company assets regresses around different mean volatility under different credit ratings. By calculating the value of corporate bonds under such asset fluctuations, the risk of credit rating migration with random volatility will be evaluated. In order to build the complete evaluation model, we introduce a special zero-coupon coupon to hedge the risks caused by the randomness of volatility. Then the partial differential equation of the corporate bond value can be derived, with continuous first-order partial derivatives about assets on the boundary of the credit rating migration. Under the new model, through the ADI difference method, the numerical solution of the corporate bond value is obtained and then the influence of the parameters and the financial significance are analyzed.

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