摘要
假设股票价格变化过程服从几何分数布朗运动,建立了分数布朗运动下的亚式期权定价模型.利用分数-It-公式,推导出分数布朗运动下亚式期权的价值所满足的含有三个变量偏微分方程.然后,引进适当的组合变量,将其定解问题转化为一个与路径无关的一维微分方程问题.进一步通过随机偏微分方程方法求解出分数布朗运动下亚式期权的定价公式.最后利用权证定价原理对稀释效用做出调整后,得到分数布朗运动下亚式股本权证定价公式.
Assuming that the process of stock price follows the geometric fractional Brownian motion,this paper constructs the pricing model for Asian option under fractional Brownian motion.The three-dimensional partial differential equation which the Asian option should be satisfied is also derived by using fractional-It-formula.Making the appropriate change of variables,this paper obtains a one-dimensional differential equation without pathdependency. Moreover,the pricing formula of an Asian option is obtained by solving the partial differential equation via stochastic partial differential equation approach.Finally,the Asian warrant pricing formula is presented using the warrant pricing principle with adjustment for the impact of dilution.
出处
《数学的实践与认识》
CSCD
北大核心
2010年第21期1-7,共7页
Mathematics in Practice and Theory
基金
国家自然科学基金(70825005)
教育部新世纪优秀人才支持计划(06-0749)
教育部人文社会科学研究规划基金项目(07JA630048
07JC630059)
