Pricing of European Option in a Fractional Brownian Motion Environment
Feng Xu
Abstract
Feng Xu
Abstract
Under the premise that stock price change follows Geometric Fractional Brownian Motion and based on the method of Esscher transform,this paper presents the formula to calculate the price of European option when the no-risk interest rate and dividend-yield rate of the stock are nonrandom functions of the time.The conclusion of this paper is consistent with Pricing of European Option on Dividend-paying Stock in a Fractional Brownian Motion Enviroment of Liu Shaoyue and Yang Xiangqun.
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Under the premise that stock price change follows Geometric Fractional Brownian Motion and based on the method of Esscher transform,this paper presents the formula to calculate the price of European option when the no-risk interest rate and dividend-yield rate of the stock are nonrandom functions of the time.The conclusion of this paper is consistent with Pricing of European Option on Dividend-paying Stock in a Fractional Brownian Motion Enviroment of Liu Shaoyue and Yang Xiangqun.
Key concepts: Fractional Brownian motion, Geometric Brownian motion, Dividend, Dividend yield, Stock (firearms), Stock price, Premise, Econometrics