分数跳-扩散O-U过程下具有违约风险的可转换债券定价

Convertible bond pricing with default risk in fractional jump-diffusion O-U process

可转换债券是金融数学核心研究内容之一.针对其定价问题,假定企业发行的股票价格和企业资产价值均服从分数跳-扩散O-U(Ornstein-Uhlenbeck)过程,基于分数布朗运动随机分析理论,利用保险精算学中保单定价的思想方法,得到了具有违约风险的可转换债券定价公式,推广了可转换债券定价理论的相关结果.

The convertible bond is one of the core problems in financial mathematics.According to its pricing problem,the pricing problem of convertible bond with default risk in fractional jump-diffusion O-U process was disscussed.With the stochastic analysis theory of fractional Brownian motion and the actuarial approach,under the assumption that stock price and firm asset price follow the fractional jump-diffusion O-U process.The pricing formula of convertible bond with default risk was obtained,and the related result of convertible bond pricing theory was generalized.