Computational Statistics

, Volume 32, Issue 4, pp 1357–1373 | Cite as

A regression-based numerical scheme for backward stochastic differential equations

  • Deng Ding
  • Xiaofei Li
  • Yiqi Liu
Original Paper


Based on Fourier cosine expansion, two approximations of conditional expectations are studied, and the local errors for these approximations are analyzed. Using these approximations and the theta-time discretization, a new and efficient numerical scheme, which is based on least-squares regression, for forward–backward stochastic differential equations is proposed. Numerical experiments are done to test the availability and stability of this new scheme for Black–Scholes call and calls combination under an empirical expression about volatility. Some conclusions are given.


Characteristic functions Least-squares regressions Monte Carlo methods European options 



We would like to thank the anonymous referees for their patience and significant suggestions which greatly improve the quality of this paper. We would also like to thank the editors for handling this paper.


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MacauMacaoChina
  2. 2.Kuang-Chi Institute of Advanced TechnologyShenzhenChina

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