Research Options Pricing Based On The Environment Of G Brownian Motion

Since the late1960s, barrier options trading appeared on the market, and had rapidly development. At present,over dozens of barrier options have growed. The present of Barrier optionsprovide a more effective method to risk managers, let they don’t have to pay for the price thatthey think can not reach. Barrier options in the financial market got rapid development sinceFisher Black, Myron Scholes and Robert Merton has achieved a breakthrough in the field of option pricing. Its relative to the standard of European and American options, flexible transactions,benefits will more conform to the investors, and the price is cheaper, so it is more popular amonginvestors. So how to give this kind of exotic option pricing has become one of the hot topic in financial mathematics field. Although the classic Black-Scholes model concise, easy to calculate,but its assumptions are more idealized,making the classic Black-Scholes model in describing thesystem risks do not consistent with the observed data. So people are constantly trying to weakenBlack-Scholes model assumptions, make better fitting financial data., A large number of empircal studies have shown that:jump diffusion model, Stochastic volatility model in the stock pricebehavior more accord with actual than the classic Black-Scholes model. Therefore, it becomethe forefront hot topic of current research,and the introduction of G Brownian motion as a random variable can be more accurately portray the volatility of financial markets, more in line with the actual situation, this article focuses pricing obstacles in the environment G Brownian motion options. Then the introduction of hybrid G Brownian motion, and gives obstacles G Brownian motion in a mixed environment of option pricing formula, the main contents are as follows:The first chapter introduces the early introduction of option pricing theory, put forward after the classic BS option pricing model, the research and development of option pricing problems, and describes the main contents of this article.The second chapter describes the basic knowledge, Brownian motion and related martingale theory, fractional Brownian motion, G expectation, G-normal distribution, G Brownian motion.Chapter Ⅲ system to pay transaction costs derived lookback options pricing by the average self-financing and Delta hedging strategies to draw geometric discrete time lookback options under the pricing formula, the results show the index and the time scale of the situation in the presence of transaction costs under option pricing plays an important role.Chapter Four times a conditional mathematical expectation should derive pricing formulas and a variety of assets and the assets of two obstacles G Brownian motion environment options maximum option pricing formula and expand to markets mixed G Brownian motion environment. Further discussed price models involved in several hedge parameters.The fifth chapter summarizes some of the conclusions of this paper and the research questions raised in this article should be taken in the future to improve some aspects.