有限体积法定价跳扩散期权模型

Finite Volume Methods for Pricing Jump-Diffusion Option Model

考虑有限体积法求解Kou模型下美式跳扩散期权.基于线性有限元空间,构造了向后欧拉和Crank-Nicolson两种全离散有限体积格式,并采用简单高效的递推公式对偏微分积分方程中的积分项进行逼近.针对美式期权离散得到的线性互补问题(LCP),采用模超松弛迭代法(MSOR)进行求解,并证明了H_+离散矩阵下算法的收敛性.数值实验表明,所构造的方法是高效而稳健的.

Finite volume methods are developed for pricing American options under Kou jump-diffusion model. Based on a linear finite element space, both backward Euler and CrankNicolson full discrete finite volume schemes are constructed. For the approximation of the integral term in the partial integro-differential equation （PIDE）, an easy-to-implement recursion formula is employed. Then we propose the modulus- based successive overrelaxation （MSOR） method for the resulting linear complementarity problems （LCPs）. The H＋ matrix property of the system matrix which guarantees the convergence of the MSOR method is analyzed. Numerical experiments confirm the efficiency and robustness of the proposed methods.