非线性Black-Scholes期权定价模型的数值模拟

摘要

Black-Scholes option pricing equation is one of the biggest achievements in modern financial theory. With the rapid development of the options market, the study of the option pricing theory is changed from linear to nonlinear. We use Newton iterative method for the numerical solution to nonlinear equations derived from the option pricing equation by implicit Euler method and finite difference method. The numerical results confirm the unconditional stability and convergence of the method.%Black-Scholes期权定价方程是现代金融理论最大的成就之一，随着期权市场的快速发展，对期权定价理论的研究由线性转变为非线性。本文利用牛顿迭代法直接解由隐式Euler方法及有限差分法离散所得的非线性代数方程组。通过MATLAB编写相应的程序，并对不同网格下求得的数值解进行对比，结果表明该方法是无条件稳定的和收敛的。