The European Option Pricing With Dividend Based On Fractional Brown Motion

The price of the option has been to the hot spot for many people to study since the Black-Scholes formula was proposed in1973. The distribution which the under-lying assets’ price to comply with is continuously improved by the development and improvement of the financial market. The traditional option pricing is mainly based on martingale method and Black-Scholes equation method. Most of the recent literature dealing with the new model of financial assets assumes that the underlying dynamics of stock prices follow a Possion jump spread process and a levy process. In the paper, stock prices exchange dynamics is based on fractional order stochastic differential equation driven by a fractional Brownian motion.first, European call option pricing with divi-dend model is established using fractional Black-Scholes equation theory, second, the solving problem of equation is transformed into the solving problem of PDE using the Fractional stochastic differential equation. finally, the option pricing is obtained based on PDE method.