The Studying Of Option Pricing Based On Wang Transform

Option pricing is one of the corn problems of mathematical finance. Black-Scholes-Merton formula is the milestone of option pricing. With an important assumption that underlying asset is subject to a geometric Brow-nian motion, this formula was established. However, the underlying asset is not subject to a geometric Brownian motion in the vast majority of cases in reality. It's characteristics are more in line with the characteristics of Fractional Brownian motion. The main research methods for option pricing in Fractional Brownian motions are insurance actuary pricing and pricing under quasimartingale. In this paper, we use a new pricing method, which is based on Wang transform. Wang proposed a general framework for pric-ing financial and insurance risk, based on a distortion function now known as the Wang transform. The Wang transform is derived from B-uhlmann economic premium principle. Wang used the Choquet integral to define the risk adjusted premium. Firstly, based on Wang transform, this paper price for European call option drived by fractional Brownian motion. Secondly, we price two new options:Capped Calls and Binary option. Thirdly, we compare Wang transform and measure transformation, finding their con-tact. Finally, this paper price the option drived by fractional Brownian motion and jump diffusion.