| 分数布朗运动驱动的期权定价模型及其风险特征 |
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| 引用本文： | 赵巍,何建敏.分数布朗运动驱动的期权定价模型及其风险特征[J].数理统计与管理,2011,30(6):1002-1008. |
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| 作者姓名： | 赵巍 何建敏 |
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| 作者单位： | 1. 淮海工学院商学院,江苏连云港222001；
2. 东南大学经济管理学院,江苏南京,210096 |
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| 基金项目： | 国家自然科学基金资助项目(70671025) |
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| 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。
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| 关 键 词： | 分数布朗运动 拟鞅定价 分数Black-Scholes模型 风险特征 |
Option Pricing Model with Stock and Exercise Price Driven by FBM |
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| ZHAO Wei HE Jian-min.Option Pricing Model with Stock and Exercise Price Driven by FBM[J].Application of Statistics and Management,2011,30(6):1002-1008. |
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| Authors: | ZHAO Wei HE Jian-min |
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| Institution: | ZHAO Wei~1 HE Jian-min~2 (1.School of Business,Huaihai Institute of Technology,Jiangsu Lianyungang 222001,China,2.School of Economics and Management,Southeast University,Jiangsu Nanjing 210096,China) |
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| Abstract: | The self-similarity and long-range dependence properties make the Fractional 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 Black-Scholes 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 ... |
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| Keywords: | fractional Brownian motion quasi-martingale pricing fractional black-scholes model risk characteristics |
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