Martingale Analysis Of Option Pricing In The Environment Of Fractional Brownian Motion

In financial statistics, Black-Scholes option pricing model to promote the general derivative securities is the important issue of modern financial statistics. The martingale approach in fractional Brownian motion and under the option pricing in the study of financial statistics plays an important role. This pin fractional Brownian motion martingale option pricing environment methods, The discussions are as follows:First, with the dividend paid for the option pricing using the equivalent martingale measure theory in the equivalent martingale measure processes of the next option; by constructing an appropriate approximation of the fractional Brownian motion the process of research environment, risk-free asset; the use of European-style options the terminal conditions of the fractional Brownian motion are given environment has a dividend-paying option pricing formula.Second, there are different lending rates to investors use self-financing of investment strategy. In the fractional Brownian motion environment, derive the corresponding lending rates with different types of power European option pricing formula. Equivalent martingale measure the use of theoretical research of the option formula, by scores based risk-neutral pricing formula construct appropriate B-S model gives the power of interest rates with different loan-type European option pricing formula.Third, taking into account the features that the market price of the stock with long-range dependence and self-similarity, cyclical changes occur over time, so set up a fractional Brownian motion model of option pricing environment. The use of martingale methods equivalent martingale measure theorem, equivalent martingale measure in the next risk-free assets and risky assets to satisfy the equation; the use ntegration and demand expectations of skills, as well as an appropriate model transformation has been fractional Brownian motion environment of European power of n-type option pricing formula. Condition of the non-periodic system's persistence; By constructing a suitable Liapunov function, it gives the sufficient condition of the system's Martingale approach to the study of the theory of pricing options could be better tools to guide people to use mathematical theory, to avoid financial market risks. This is for reducing the risk of investors in investment, and financial market stability for sustainable development has a wide range of theoretical and practical significance.