Pricing geometric asian power options in the sub-fractional brownian motion environment

Abstract

This paper aims of obtaining the closed form expressions for the prices of the geometric Asian options and power options when the payoff function is a power function. After discussing the option pricing in the sub-fractional Brownian motion environment, by the fractional Ito^ formula which is based on the theory of stochastic differential equation, the sub-fractional Ito^ formula is derived. Furthermore, the solution of the stochastic differential equation satisfied by stock prices is obtained. The stock price process is modeled well with the driving force as the sub-fractional Brownian motion. The empirical results show that the fitting effect is better than the Brownian motion.