求解广义Black-Scholes方程的指数型差分法

Exponential Time Difference Scheme for a Generalized Black-Scholes Equation

文中给出了求解广义Black-Scholes的稳定的、二阶收敛的数值方法。首先在分片一致网格上应用中心差分格式对Black-Scholes方程关于空间变量离散,然后对半离散问题应用指数时间积分法离散。此数值策略对于任意波动率和任意利率都是稳定的,并且是关于标的资产价格二阶收敛的。数值实验证实了理论结果的正确性。

In this paper we present a numerical method for a generalized Black-Scholes equation.The numerical method utilizes a central difference scheme on a piecewise uniform mesh with respect to the spatial variable combined with an exponential time integration scheme.Our scheme is stable for arbitrary volatility and arbitrary interest rate,and is second-order convergent.Numerical results support the theoretical results.