有限体积法定价跳扩散期权模型

Finite Volume Methods for Pricing JumpDiffusion Option Model

摘要:

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.

Abstract:

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 CrankNicolson 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.