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求解跳-扩散期权定价方程的隐显Runge-Kutta方法
李子丰, 王晚生
上海师范大学 数理学院, 上海 200234
摘要:
金融衍生品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.
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
DOI:10.3969/J.ISSN.1000-5137.2022.03.004
分类号:O241.8
基金项目: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)
IMEX Runge-Kutta method for solving jump-diffusion option pricing equation
LI Zifeng, WANG Wansheng
Mathematics and Science College, Shanghai Normal University, Shanghai 200234, China
Abstract:
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.
Key words:  option pricing  partial integro-differential equations  extrapolated  variable step-sizes implicit-explicit (IMEX) Runge- Kutta methods  finite difference method