分红存在上界含信用等级迁移的定价模型

A Pricing Model of Credit Rating Migration Included in Existence of an Upper Bound on Dividends

摘要:

考虑在债券发行方可能发生信用等级迁移情况下公司资产分红存在上界的零息票债券的定价问题。根据公司资产的数量将公司分为高低两种信用等级状况，公司资产价值变化满足带有红利率的几何Brownian运动，同时考虑到对公司资产的分红有预期计划，当累计红利数达到预期值时，公司资产价值变化便满足普通几何Brownian运动。通过计算此模型下公司债券的价值，进而评估信用等级迁移的风险，同时利用对冲推导出在信用等级迁移边界上的条件。建立创新的含信用等级迁移的风险评估模型，进而利用特征线隐格式差分法进行求解，得到公司资产价值的数值解并分析其金融意义。

Abstract:

This paper considers the pricing of zero-coupon bonds with an upper bound on the dividends on the firm’s assets in the presence of a possible credit rating migration of the bond issuer. Firms were classified into two credit rating statuses， high and low based on its assets， and the change in the value of the firms’ assets satisfied the geometric Brownian motion with the dividend rate， and the change in the value of the firms’ assets satisfied the ordinary geometric Brownian motion when the number of cumulative dividends reached the expected value， taking into account that there was a plan for expected dividends on the firms’ assets. By calculating the value of corporate bonds under this model， the risk of credit rating migration was then assessed， while hedging was used to derive the conditions at the credit rating migration boundary. An innovative risk assessment model including credit rating migration was established， and then the eigenline implicit format difference method was used to solve it， and the numerical solution of the company’s asset value was obtained and its financial significance was analyzed.