Study On New Options Pricing Under The Fractional Jump-diffusions

In the financial derivative products, new options with strong flexibility, which can be designed according to specific requirements and be widely used, it plays an important role in derivative products. Competitions force the financial structure of financial markets to accelerate innovation. Therefore, it is very important to study the problem of new option pricing.This paper introduces the development of option pricing and its related concepts, current research and significance of the thesis about the options market have been described in detail,and then focuses on the theory of stochastic processes that are related to this article. In addition,by selecting four representative stocks, through the numerical experiments and analysis on its data, we obtain that fractional Brownian motion with jumps is better to describe changes of stock price. Furthermore, we select the two-way option, and type power option to study by means of the actuarial method and other methods, on these bases, we obtain pricing formulas of two-way option, and power option, these pricing theory lay the foundation for the study of other new options pricingThe third chapter content that calculate the Hurst index through the numerical experiments and analysis by ORINGE and MATLAB, we come to conclusion that fractional Brownian motion with jumps is better to describe changes of stock price. which lay the foundation for the study of new options pricing.The study of new options pricing model is in the fourth chapter, the theoretical innovation that we assume asset is subject to fractional Brownian motion with jumps,considering the situation of dividend payments, and using the actuarial method, we obtain the pricing formulas of two-way option with fixed or change exercise price. In addition, the power option is gotten with stochastic integral method. Compared to other methods,stochastic integral method is easier to understand.