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基于鞅方法的分数Brown运动模型的期权定价 被引量：6

Options Valuating of FBM Model Based on the Martingale Method
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摘要 本文利用基础资产价格过程的逼近过程,研究了一类Hurst指数属于(1/2,1)的分数Brown运动模型,通过逼近过程的鞅性,获得了FBM市场的等价鞅测度通过鞅测度变换获得了FBM下的期权定价控制方程和欧式期权的解析公式,改进了部分已有的结果. In this paper,a fractional Brownian motion model which Hurst index belongs to （1/2,1） has been studied by using the martingale property of an approximate stochastic process. The equivalent martingale measure of FBM approximate market has been found,the control equation and close solution of Europe options has been obtained. These results improved some conclusions.
作者 梅正阳 杨玉孔
机构地区 华中科技大学数学与统计学院
出处 《应用数学》 CSCD 北大核心 2008年第4期727-730,共4页 Mathematica Applicata
关键词 HURST指数 分数Brown运动 等价鞅测度 期权定价 Hurst index Fractional Brownian motion Equivalent martingale measure Options valuate
分类号 F830.9 [经济管理—金融学] O211.62 [理学—概率论与数理统计]
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参考文献8

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同被引文献47

  • 1王俊,罗猛.简析等价鞅测度及其应用[J].统计与决策,2004,20(9):119-121. 被引量：1
  • 2刘韶跃,杨向群.分数布朗运动环境中欧式未定权益的定价[J].应用概率统计,2004,20(4):429-434. 被引量：50
  • 3邵宇.微观金融学及其数学基础[M].北京:清华大学出版社,2005.
  • 4ELLIOT R J, VAN DER HOEK J. A general white noise theory and applications to finance[J]. Math Finance,2003, 13(2) :301-330.
  • 5HU Y, OKSENDAL B. Fractional white noise calculus and applications to finance[J]. Infin Dimens Anal Quantum probab Relat,2003,6(1) : 1-32.
  • 6SATTAYATHAM P, INTRARASIT A, CHAIYASENA A P. A fractional-Black-Schole with jumps[J]. Vietnam JournaI of Mathematics,2007(35) : 1-15.
  • 7THAO T H. An approxiamte approach to fractional analysis for finance[J]. Nonlinear Analysis: Real World Applications, 2006(7) : 124-132.
  • 8SHREVE S E. Stochastic Calculus for Fianace Ⅱ [M]. Berlin: Springer,2004.
  • 9Elliot R J, Van Der Hoek J. A general fractional white noise theory and applications to finance[J] . Math Finance, 2003,13(2) : 301-330.
  • 10Hu Y, Oksendal B. Fractional white noise calculus and applications to finance[J]. Infin Dimens Anal Quantum Probab and Relat Top, 2003,6 : 1-32.

引证文献6

二级引证文献16

应用数学
2008年 第4期

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