The price of the option has been to the hot spot for many people to study since the Black-Scholes formula was proposed in 1973.The distribution which the underlying assets'price to comply with is continuously improved by the development and improvement of the financial market.In 1991 Peters who is a American scientist first proposed the concept of the Fractal market,and pointed out that fractional Brownian motion can be more accurately portray the financial market volatility.We know that the price of the underlying assets is a time series,the variable for studying the this series should change with time.Firstly,this paper is based on the European option pricing which is under the environment of the mixed fractional Brownian motion(formed by a fractional Brownian motion and a standard Brownian motion),then let the parameters change with the time,so we can obtain the new conclusion.Secondly,we obtain the European option pricing formula in the case of the underlying asset subject to Mixed fractional Brownian motion(formed by many combinations of fractional Brownian motion),also we derivde the pricing of the mixed options in this case. |