The pricing formula of indexed executive stock options in fractional motion environment

Abstract：In order to solve the problem that stock price can not be simulated accurately by Geometry Brownian Motion, the simulative formula of stock price which Geometric Fractional Brownian Motion was derived.Based on risk-neutral price principle and via two-dimensional integral method, the formula of indexed executive stock options was obtained when the underlying asset price obeyed the Geometric Fractional Brownian Motion.Compared with the traditional indexed stock options, the formula of sensitivity parameter in Fractional Brown Motion environment was obtained.And compared with the results in the known articles, the formula of fractional indexed executive stock options is consistent with the traditional one when Hurst parameter in Fractional Brown Motion equals 0.5.

Keyword：executive stock options;exercise price;geometry fractional brownian motion;risk-neutral;