资产波动率为随机的信用等级迁移风险评估模型

doi:10.12341/jssms21346

系统科学与数学 ›› 2022, Vol. 42 ›› Issue (2): 304-317.DOI: 10.12341/jssms21346

资产波动率为随机的信用等级迁移风险评估模型

梁进, 周汇慧

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.

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梁进, 周汇慧. 资产波动率为随机的信用等级迁移风险评估模型[J]. 系统科学与数学, 2022, 42(2): 304-317.

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

School of Mathematical Sciences, Tongji University, Shanghai 200092

Received:2021-06-29 Revised:2021-09-14 Online:2022-02-25 Published:2022-03-21

以公司债券为手段，评估具有随机波动率的信用等级变换的风险.根据公司资产的多少将公司划分为高低两种信用等级，并假设公司资产的变化满足Heston随机波动率模型，且波动率在高低等级下围绕不同的均值波动回归.通过计算这样的资产波动下公司债券的价值，来评估具随机波动率的信用等级变换的风险.利用一张特殊的零息票来对冲由波动率的随机性造成的风险，推导出在信用等级迁移边界上，债券价值关于资产的一阶偏导数连续的偏微分方程.在所建的新模型下，利用ADI差分方法对偏微分方程进行求解，得到公司债券价值的数值解并分析了各个参数的影响和金融意义.

关键词： 信用等级迁移风险, 随机波动率, Heston 模型, 债券价值

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.

Key words: The risk of credit rating migration, stochastic volatility, Heston model, corporate bond value

MR(2010)主题分类:

91B28
91G40

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