Option Pricing Research Based On Mixed Fractional Brownian Motion

Academic circle has carried out a series of research for financial derivatives such as option pricing work.In many studies,the underlying asset price follows a fractional Brownian motion which has the thick tail and long-term correlation properties,and in the actual financial market,there are lots of costs and dividend,it is difficult to learn the option pricing.Therefore,this paper studies European option,Asian option,power Asian option pricing under mixed fractional Brownian motion.The main results are as follows:(1)European call option pricing model with fixed transaction cost and dividend was obtained under mixed fractional Brownian motion using the risk neutral pricing theory.We obtain the option value through the variable substitution,at the same time,deduce the put option value according to call-put parity formula.The impact of the volatility and fixed transaction cost was discussed by the numercal examples.(2)We established Asian option model under mixed fractional Brownian motion and obtained the analytical solutions.At the same time,through deducing the call-put parity formula,the put option is get.Finally,the influences of Hurst index,risk-free interest,time on the option value with the help of Matlab software.(3)We study power Asian option pricing with friction factor based on mixed fractional Brownian motion.First,A model of power Asian option pricing model is estalished by constructing a proper option portfolio,using risk neutral pricing theory.Then we use the variable subsitution to convert it to heat conduction equation in order to obtain power Asian option pricing formula.Finally,we discuss the impact of corresponding market parameter especially on the option value by numerical analysis.(4)This paper deduces the value of option under standard Brownian motion,fractional Brownian motion and mixed fractional Brownian motion states and numerical examples show the influence of parameters and the stability.