双分数跳-扩散Ornstein-Uhlenback过程下可转换债券定价

Convertible bond pricing model in bi-fractional jump-diffusion Ornstein-Uhlenback process

随着金融衍生品的发展,出现了高级金融衍生品,可转换债券就是其中之一.双分数布朗运动是更一般的高斯过程,能描述更多的随机现象;而Ornstein-Uhlenback过程是一类重要的移动平均过程.本文考虑突发事件的影响,假定股票预期收益率和股价波动率都为常数,构建双分数跳-扩散Ornstein-Uhlenback过程下的模型,应用保险精算方法,获得可转换债券的定价公式.

With the on-going development of financial derivatives,convertible bond is one of the emergence of advanced financial derivatives.The binary fractional Brownian motion is a more general Gaussian process,which can describe more random phenomena.The Ornstein-Uhlenback process is an important type of moving average process and is applied in this study.Considering the impact of emergencies,the authors assume that both the stock return and the volatility of the stock price are constant.The model under the bi-fraction jump-diffusion Ornstein-Uhlenback process is established,and the actuarial method is used to obtain the pricing formula of convertible bonds.