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欧氏看涨期权定价问题的一种有效七点差分GMRES方法
引用本文:顾传青,康颖.欧氏看涨期权定价问题的一种有效七点差分GMRES方法[J].应用数学与计算数学学报,2014(4):518-528.
作者姓名:顾传青  康颖
作者单位:上海大学理学院,上海200444
基金项目:国家自然科学基金资助项目(11371243);上海市教委科研创新重点资助项目(13ZZ068);上海市重点学科建设资助项目(S30104)
摘    要:用有限差分方法研究欧氏看涨期权定价问题.首先,将Black-Scholes方程通过等价代换化成一个标准的抛物型偏微分方程.其次,在求解区域构造时间精度为O(△τ^3)、空间精度为O(h^6)的差分格式,并通过Fourier分析方法证明该差分格式是无条件稳定的;边界区域选用精度较高、稳定性好的Crank-Nicolson格式,建立迭代方程.然后,用GMRES(generalized minimal residual)方法求解该方法.最后,给出一个欧氏看涨期权的数值算例,并与解析解进行比较,验证差分格式的有效性.

关 键 词:Black-Scholes方程  欧氏看涨期权定价  有限差分  Fourier分析  GMRES方法

Effective seven-point difference GMRES method for European call option pricing
GU Chuan-qing,KANG Ying.Effective seven-point difference GMRES method for European call option pricing[J].Communication on Applied Mathematics and Computation,2014(4):518-528.
Authors:GU Chuan-qing  KANG Ying
Institution:(College of Sciences, Shanghai University, Shanghai 200444, China)
Abstract:In this paper,we study European call option pricing by the finitedifference method.First,we equivalently transform the Black-Scholes equation into a standard parabolic partial differential equation.Second,we construct a difference scheme over the inner domain,with the order O(h^6 + △τ^3),and it is proved to be unconditionally stable by the Fourier analysis.The Crank-Nicolson method with high precision and good stability is adopted for border domain.Therefore,we present an algebraic equation.Third,we adopt the GMRES(generalized minimal residual) method to solve the equation.Last,the numerical example verifies the efficiency.
Keywords:Black-Scholes equation  European call option pricing  finite difference  Fourier analysis  GMRES method
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