A regression-based Monte Carlo method to solve two-dimensional forward backward stochastic differential equations

Advances in Difference Equations

article

Li, Xiaofei¹  Wu, Yi⁴  Zhu, Quanxin⁵  Hu, Songbo⁶  Qin, Chuan⁷ 

[1] Zhuhai Da Hengqin Science and Technology Development Co Ltd;Hubei Key Laboratory of Applied Mathematics, Faculty of Mathematics and Statistics, Hubei University;Hengqin Finance Research Institute of Jilin University;School of Information and Mathematics, Yangtze University;School of Mathematics and Statistics, Hunan Normal University;Jiangxi Province Key Laboratory of Preventive Medicine, School of Public Health, Nanchang University;College of Engineering and Technology, Yangtze University

关键词: Forward backward stochastic differential equations;    Fourier cos-cos transform;    Characteristic functions;    Least-squares regressions;    Monte Carlo;   

DOI  :  10.1186/s13662-021-03361-5

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

The purpose of this paper is to investigate the numerical solutions to two-dimensional forward backward stochastic differential equations(FBSDEs). Based on the Fourier cos-cos transform, the approximations of conditional expectations and their errors are studied with conditional characteristic functions. A new numerical scheme is proposed by using the least-squares regression-based Monte Carlo method to solve the initial value of FBSDEs. Finally, a numerical experiment in European option pricing is implemented to test the efficiency and stability of this scheme.

【 授权许可】

CC BY