| 股价遵循分数布朗运动的最大值期权定价模型 |
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| 引用本文： | 赵巍. 股价遵循分数布朗运动的最大值期权定价模型[J]. 数学的实践与认识, 2011, 41(3) |
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| 作者姓名： | 赵巍 |
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| 作者单位： | 淮海工学院商学院,江苏,连云港,222001 |
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| 基金项目： | 淮海工学院引进人才科研启动基金(KQ09012) |
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| 摘 要： | 分数布朗运动由于具有自相似和长期相关等分形特性,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分数Black--Scholes市场;接着在分数风险中性测度下,利用随机微分方程和拟鞅定价方法给出了分数Black-Scholes定价模型;进一步放松初始假定,讨论了多个标的情形的最大值期权定价问题.研究结果表明,与标准期权价格相比,分数期权价格要同时取决于到期日和Hurst参数.
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| 关 键 词： | 分数布朗运动 拟鞅定价 分数Black-Scholes模型 最大值期权 |
Option Pricing on the Maximum of Stock Driven by FBM |
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| ZHAO Wei. Option Pricing on the Maximum of Stock Driven by FBM[J]. Mathematics in Practice and Theory, 2011, 41(3) |
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| Authors: | ZHAO Wei |
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| Affiliation: | ZHAO Wei (School of Business,Huaihai Institute of Technology,Lianyungang 222001,China) |
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| Abstract: | For Brownian motion is the drawback of option pricing model,this paper considers the assert price followed geometric FBM.Using of quasi-martingale method based on the risk neutral measure,this paper solved fractional Black-Scholes model and the Option on the Maximum of n Assert.The result showed fractional option price,compared to classical option price,depends on maturity time and Hurst parameter. |
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| Keywords: | Fractional Brownian motion quasi-martingale pricing fractional Black-Scholes model option pricing on the maximum |
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