分数布朗运动环境下可转换债券定价模型

Convertible bonds pricing model in fractional Brownian motion environment

假定股票价格方程遵循分数布朗运动驱动的随机微分方程,利率、波动率、支付红利率均为时间的确定性函数.利用分数布朗运动随机分析理论,建立了分数布朗运动环境下具有支付红利的金融市场数学模型,得到了分数布朗运动环境下具有支付红利的可转换债券的定价公式.

This paper assumed that asset price satisfied stochastic differential equation driven by the fractional Brownian motion, and interest rate, volatility rate and dividend rate were functions of time. The financial market mathematical model with dividend was built in the fractional Brownian motion environment. Using the stochastic analysis theory for the fraction- al Brownian motion, the pricing formula of convertible bonds was obtained.