The Model Of Stochastic Volatility In Fnancial Market

The modern financial theory is growing up constantly by the development of the financial market, its prominent characteristic is introducing theory and method of mathematics and physics in financial economics constantly to study taking precautions against and control fiancial risk, operationg of capital marketing, structure and pricing of the capital assets with them. From the investigation of the quantity process of the modern finance, it is found that a key question of the financial theory lands on fluctuation all the time, which is the background of the studied.The fluctuation is not only the important index assessing the market, but also the importance that people carry on investment decision, assets assessment, option fixing the price at the time of risk management. Therefore, how to accurate and predicte the fluctuation of market has been always the focus of practice circle and the circle of theory all the time for many years. The development of modern econometrics methodology, has analyzed and offered the solid methodology foundation for the dynamic modeling of the fluctuation, have initiated unusually brilliant various theories and methods about fluctuation modeling later on. With the deepening of the study, under the numerous efforts of scholars and experts, fluctuation model makes a prominent progress. Especially analyzing the development of studying offers the more effective mathematics tool for financial market at random. In the text, based on the B-S model background, it is studied the function of setting up random differential equation in financial market of fluctuating.It is introduced and analyzed financial quantity progress and various fluctuation rate model of research partially, the characteristic of the fluctuating rate of financial market in the part I of the text.In the part II, B-S model is presented providing the price formula under fixed value fix of fluctuation option, and analyzing the real example of the bid index of the Chinese stock of 2004, 2005, relatively finding the better change within 2004 and 2005 of two markets by the description of geometirc Brownian movement with the real data.In the third part, popularizing B-S model, setting up pricing model in random of the fluctulation rate assets price obeying limited Markov chain, through analyziing the differential equation in the model, providing the pricing formula.