Fractional Stochastic Differential Equation Theory And Its Applications To Option Pricing

Against the backdrop of economic globalization,finance being the core of the China's economy became marked.Option is one of the most important derivative securities in the financial market,the pricing has been a hot and frontier issues of research in mathematical finance.In recently years,the applying stochastic differential equations to the financial field have became a hot topic and a growing number of instances show that the stochastic differential equation has become a very practical tool among the study of option pricing.Since the BS model came out,it has been widely approved by the researchers on option pricing.With the progress of the study,it also has been improved constantly.Howe ver,a largenumber of studies show that,in the actual financial market,the classical BS mode 1 can't perfectly describe the process of stock price,while the results through studying optio n pricing,using the method of fractional Brown motion,are more in line with the actual situa tion.Based on this,this paper mainly studies the fractional stochastic differential equation the ory,and its application in option pricing.The main work of this paper is as follow:The first chapter is introduction,we introduce the process of the option pricing theory,as well as the fractional stochastic differential equation theory.In order to make full use of the fractional stochastic differential equation theory,we give a detailed introduction for the basic knowledge in the second chapter.The main content of the paper is chapter three,chapter four and chapter five.In the third chapter,we construct different pricing model.Firstly,by applying no-arbitrage theory and hedging principle,we get the fractional Black-Scholes modle and obtain option pricing formula through stochastic analysis theory;Secondly,we discuss Esscher transformation model.By using Esscher transform method and quasi-martingale pricing method,we get the European option pricing formula.The fourth chapter mainly deals with option pricing problem with transaction costs under the fractional Brown motion.By using delta-hedging theory in a discrete time setting,a European call option pricing formula is obtained and analyze the influence of time scaling ?t and Hurst exponent H on option pricing.In the fifth chapter,we consider the other option pricing methods:By applying the variational iteration method,an approximation solution of pricing formula with transaction costs is get.In discrete time we get time-change fractional B-S model and discuss option pricing under transaction costs when time step ?t is given.