求解Merton跳扩散模型的隐显BDF2方法  

IMEX-BDF2 Method for Solving Merton Jump-Diffusion Model

作　　者：方华 王晚生 FANG Hua;WANG Wansheng(School of Mathematics and Computational Science,Changsha University of Science and Technology,Changsha 410114,China)

机构地区：[1]长沙理工大学数学与统计学院,长沙410114

出　　处：《湖南理工学院学报（自然科学版）》2018年第1期1-6,25,共7页Journal of Hunan Institute of Science and Technology(Natural Sciences)

基　　金：国家自然科学基金项目(11771060;11371074)

摘　　要：Black-Scholes期权定价方程是现代金融理论最伟大的成就之一,推动了全球金融市场的发展.本文以Merton提出的带有跳扩散过程的偏积分微分方程为研究对象,对空间微分算子使用有限差分方法离散.由于空间积分算子的非局部性质,为减少工作量,采用显式时间离散进而推导了二阶变步长隐显BDF方法,并通过数值例子验证了该方法的有效性.Black-Scholes option pricing equation is one of the biggest achievements in modem financial theory.In this paper,we studied the partial integro-differential equation with jump-difiusion process proposed Merton.The discretization of spatial differential operators is by finite difference method.In view of the non-local property of the spatial integral operator,we use explicit time discretization for reducing the compute cost.We further derived the variable step-size IMEX-BDF2 method for solving Merton jump-difEusion model.Numerical example illustrates the effectiveness of the proposed method.

关 键 词：Merton跳扩散模型 期权定价 有限差分法 二阶变步长隐显BDF方法 

分 类 号：O241.8[理学—计算数学]