| Against the backdrop of economic globalization, Finance being the core of the China's economy became marked. Financial issues will be the primary strategic problem of economic and social development, reform, stability. It must be handled with careful. Options are derivatives of financial market.Its theoretical study are important in theory and practice.It has an extremely important application in the development of financial markets and preventing financial risks.First, The paper give a detailed introduction for the main results and current research focus of the option pricing theory, as well as financial risks.And expound the practical significance of the subject in depth. Then, The paper introduce the concept and nature of options. From the advantages and disadvantages of the efficient market theory(EMH),The fractal market hypothesis(FMH) which based on nonlinear market structure be introduced and be compare with the EMH. Then introduce the definition and nature of the Brownian motion and fractional Brownian motion.Next, The paper study the general form and basic properties of the subject of fractional stochastic differential equations, whose underlying assets subject to fractional Brownian motion.And study the fractional Black-Scholes formula, fractional Black-Scholes differential equations and their deduction. The paper focus on the study of the barrier option and warrant pricing formula under fractional Brownian motion.Again,The paper gives an overview of the basic principles, calculation methods an application of VaR and R/S,according to the idea of financial risks and the option pricing theory of fractal market.As we known,The international financial crisis,that caused by the US subprime mortgage crisis,is not yet bottomed out and still spreading. Finally, according to the current situation particularly,The paper consider the cause and revelation of international financial crisis in depth by mathematical logic and the excellent idea of many scholars. |
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