随机波动下障碍期权定价的有限差分方法

Finite difference method for barrier option pricing under stochastic volatility

为有效求解随机波动影响下,障碍期权定价的二维对流扩散方程的初值边值问题,采用非均匀有限差分近似方法,构造了非均匀空间网格,利用泰勒级数展开式导出了非均匀网格上的一阶偏导、二阶偏导以及混合偏导项的差分格式,对离散得到的常微分方程组采用Craig-Sneyd格法迭代求解,通过数值实验将所得结果同蒙特卡洛方法进行了比较.研究结果表明,非均匀有限差分方法是求解障碍期权定价问题的一种稳健、有效的数值方法.

In order to effectively solve the initial-boundary value problem of a two-dimensional convection-diffusion equation for barrier option pricing with stochastic volatility, this paper uses a non-uniform finite difference approximate method, and constructs the non-uniform space grids. Taylor series expansion is used to obtain difference approximation of the first derivative, second derivative and mixed derivative on the non-uniform space grids. This paper solves the obtained ordinary differential equations using Craig-Sneyd iterative scheme, and compares the outputs with Monte Carlo method by some numerical experiments. Numerical results show that the non-uniform finite difference is a robust and effective numerical method for barrier options pricing.