期刊论文

IMEX-BDF2 Method for Solving Merton Jump-Diffusion Model

中文

湖南理工学院学报(自然科学版)

1672-5298

2018

31

1

1-6+25

10.16740/j.cnki.cn43-1421/n.2018.01.001

11771060:国家自然科学基金 11371074:国家自然科学基金

本校为第一机构

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 e...