混合双分数布朗运动环境下支付红利的欧式期权定价

Pricing European Option with Dividends Under Mixed Bi-fractional Brownian Motion

假定标的资产价格由混合双分数布朗运动驱动时,考虑在买卖期权交易过程中支付红利时欧式看涨期权的价值。在离散时间情景下,运用自融资风险对冲思想得到期权价值满足的偏微分方程。为了便于求解,通过Mellin变换将偏微分方程转变为一般的常微分方程,结合欧式看涨期权的终端条件,最终得到偏微分方程的解析解,即欧式看涨期权定价公式。

Assuming that the price of the underlying asset is driven by mixed bi-fractional Brownian motion,this paper considers the value of a European call option with paying dividends in the trade process of buyingand selling options.By a self-financing risk hedging argument in a discrete-time setting,the partial differentialequation for the option value is obtained.In order to facilitate is solution,the partial differential equation istransformed into ordinary differential equation through Mellin transform.Combined with the terminal conditionsof the European call option,the analytic solution for the partial differential equation is derived.The pricingformula of the European call option with dividends under mixed bi-fractional Brownian motion is obtained.