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中文摘要：
分数布朗运动由于具有自相似或长记忆等分形特性，已成为数理金融研究中更为合适的工具。通过假定股票价格服从几何分数布朗运动，构建了Ito型分数Black-Scholes市场；随后基于拟鞅定价方法，求解了分数风险中性测度下的期权定价模型；进而放松执行价格为固定值的假定，研究了股价和履行价共同受分数布朗运动驱动的期权定价模型。数值模拟研究表明，长记忆参数值越大，对投资者和券商的避险策略越有利。
英文摘要：
The self-similarity and long-range dependence properties make the Practional Brownian motion a suitable tool in different applications like mathematical finance. This paper used the hypotheses that assert price followed geometric FBM to construct the Ito fractional Blaek-Seholes market. Using of quasi-martingale method based on the fractional risk neutral measure, this paper solved fractional Black-Scholes model. Moreover Option Pricing model with stock and exercise price droved by FBM was discussed. The result showed that the larger of long memory parameter value, the better for investor and securities trader to hedging.
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