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求解Black-Scholes方程时截断误差的分析 被引量:2

Analysis ofthe Truncated Errorin Solving the Black-Scholes Equation
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摘要 研究了在对 Black- Scholes方程求数值解时应如何对边界条件进行合理的离散方可获得理想的数值结果这一有价值的问题 .通过理论和数值模拟分析可知 ,一个传统的边界条件处理方法会使截段误差在一定范围内快速积累 ,从而使数值结果失真 .对传统处理方法作了修改 ,使新算法更有效 ,并进一步给出了一个用区域分解方法求解离散后线性代数方程组的迭代算法 . This paper introduced an approach to approximating the related boundary conditions with small truncated errors which is useful for the numerical solution of the well- known Black- Scholes equation in mathematical finance.According to the theoretical and numerical analysis,it found that the traditional method would lead to inaccuracy due to the accumulation of the truncated error ateach step.Furthermore, this paper proposed a domain decomposition method to solve the resulting algebraic system.This iterative method has good convergence rate but does not depend on the choice of the related parameters.
出处 《上海交通大学学报》 EI CAS CSCD 北大核心 2000年第8期1126-1129,共4页 Journal of Shanghai Jiaotong University
基金 国家自然科学基金资助项目!(79790 1 30 1 990 1 0 1 8)
关键词 载断误差 显式差分格式 B-S方程 计算 Black- Scholes equation truncated error explicit difference scheme domain decomposition
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参考文献2

  • 1唐旭(译),Financial engineering,1998年
  • 2叶中行,数理金融.资产定价理论与金融决策分析,1998年

同被引文献10

  • 1田振夫.泊松方程的高精度三次样条差分方法[J].西北师范大学学报(自然科学版),1996,32(2):13-17. 被引量:10
  • 2Joseph S,Victor G.The Mathematics of finance:modeling and hedging[M].Thomson Learning.2001.
  • 3Burrage K.Burrage P M,Tian T.Numerical methods for strong solutions of stochastic differential equations:an overview[J].The Royal Society,2004,460:373402.
  • 4陆金甫,关治.偏微分方程数值解法(第2版)[M].北京:清华大学出版社,2003.
  • 5Gerge M J,Marat V K,Stephen D Y.Two-state option pricing:binomial models revisited[J].The Journal of Futures Markets,2002,22(7):601 626.
  • 6陆金甫关治偏微分方程数值解法[M].
  • 7Joseph Stampfli,&Victor Goodman.The Mathematics of Finance:Modeling and Hedging. Thomson Learning . 2001
  • 8K.Burrage,,P.M.Burrage,and T.Tian.Numerical methods forstrong solutions of stochastic differential equations:an overview. The RoyalSociety . 2004
  • 9Gerge M Jabbour,,Marat V Kramin,,Stephen D.Young.Two-stateOption Pricing:Binomial Models Revisited. The Journal of Futures Mar-kets . 2002
  • 10田振夫,张艳萍.扩散方程的高精度加权差分格式[J].中国科学技术大学学报,1999,29(2):237-241. 被引量:10

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