求解跳-扩散期权定价方程的隐显Runge-Kutta方法  

IMEX Runge-Kutta method for solving jump-diffusion option pricing equation

作　　者：李子丰 王晚生 LI Zifeng;WANG Wansheng(Mathematics and Science College,Shanghai Normal University,Shanghai 200234,China)

机构地区：[1]上海师范大学数理学院,上海200234

出　　处：《上海师范大学学报（自然科学版）》2022年第3期277-283,共7页Journal of Shanghai Normal University(Natural Sciences)

基　　金：国家自然科学基金(11771060);上海市自然科学基金(20ZR1441200);上海市科技计划项目(20JC1414200)。

摘　　要：金融衍生話的定价研究一直是金融数学研究的难题之一.随着期权定价理论的不断发展和完善,跳-扩散期权定价模型的研究更是成为热点,该模型是一个无界区域上的偏积分微分方程.研究跳-扩散模型下欧式期权定价问题的外插变步长隐显(IMEX)Runge-Kutta方法,结合有限差分空间离散,并通过数值实验验证该方法的有效性.The study on financial derivatives pricing has been one of the difficult issues in financial mathematics.With the continuous development and improvement of option pricing theory,the research on the jump-diffusion option pricing model has become a hotspot,which is a partial integro-differential equation over an unbounded region.Study the extrapolated variable step-sizes implicit-explicit(IMEX)Runge-Kutta methods combined with finite-difference space discretization for European option pricing problems under the jump-diffusion model,and the effectiveness of the methods is verified by numerical experiments.

关 键 词：期权定价 偏积分微分方程 外插 变步长隐显(IMEX)Runge-Kutta方法 有限差分法 

分 类 号：O241.8[理学—计算数学]