求解Black-Scholes方程时截断误差的分析

Analysis ofthe Truncated Errorin Solving the Black-Scholes Equation

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.