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股价受分数布朗运动驱动的混合期权定价模型(
)
《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]
- 卷:
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第33卷
- 期数:
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2010年01期
- 页码:
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6-10
- 栏目:
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数学
- 出版日期:
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2010-03-20
文章信息/Info
- Title:
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Pricing of Compound Option Model With Stock Price Driven by FBM
- 作者:
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赵巍;
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淮海工学院商学院
- Author(s):
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Zhao Wei
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School of Business,Huaihai Institute of Technology,Lianyungang 222001,China
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- 关键词:
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- Keywords:
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- 分类号:
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F830.91;F224
- 摘要:
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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.本文通过假定股票价格服从几何分数布朗运动,构建了It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(quasi-martingale)定价方法给出了分数Black-Scholes定价模型;进而讨论了股价受分数布朗运动驱动的混合期权定价模型.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.
- Abstract:
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The se l-f sim ilar ity and long- rang e dependence properties m ake the Frac tiona l B rown ian m otion a suitable too l in d ifferen t applications likem a them atical finance. Th is paper used the hypotheses that asse rt price follow ed geome tr ic FBM to construct the It? fractional B lack-Scholes m arket. U sing of quas-i m artinga lem ethod based on the fractiona l r isk neutra lm easure, this paper so lved fractiona l Black-Scho les m ode.l M oreove r pr ic ing of com pound option mode l w ith stock pr ice dr iven by FBM w as discussed. The result show ed frac tiona l option pr ice, compared to c lassical option price, depends on m atur ity tim e and H urst parameter.
更新日期/Last Update:
2013-04-08