分数布朗运动下带红利的欧式期权定价

摘要

基于股票价格遵循有分数布朗运动驱动的分数阶随机微分方程.运用Black-Scholes方程理论建立带红利的欧式看涨期权定价模型,根据分数阶随机微分方程理论将方程的求解问题转化为偏微分方程的求解问题,给出期权定价的解析解.%A basis was taken that the stock price should obey fractional-oder stochastic differential equations with the driving of fractional Brown motion. By using Black-Scholes equation and theory, an European option pricing model with expected price rising was established. Then the solution of the fractional-order stochastic differential equations was transformed into solving a partial differential equation and an analytic solution was given for the option pricing.