| "Financial Mathematic,Financial Project and Financial Management"constitute a significant research project specified by the National Foundation of Natural Science of China,in which option pricing theory is a problem of leading edge as well as a hot one.In order to satisfy the finance market and the different investor especial needs,and keep away the risk which manyinvestors might face,standard Brownian motion can not satisfaction daily requirement and fractional Brownian motion is displayed to advantage for such complex issues.This thesis mainly deals with the pricing problem of the barrier options, which is a kind of path dependent options in fractional Brownian motion. Such facts showed that the stock has two properties:the self-similar properties, the long-range dependent properties.However the fractional Brownian motion satisfied the two properties.And we present the price model of the barrier options by using the Ito formula. Besides, This thesis use the price model of the barrier options to present the price model of the correction barrier options and the price model of double barrier options in fractional Brownian motion. |
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