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A regression-based numerical scheme for backward stochastic differential equations

Author

Listed:
  • Deng Ding

    (University of Macau)

  • Xiaofei Li

    (University of Macau)

  • Yiqi Liu

    (University of Macau
    Kuang-Chi Institute of Advanced Technology)

Abstract

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.

Suggested Citation

  • Deng Ding & Xiaofei Li & Yiqi Liu, 2017. "A regression-based numerical scheme for backward stochastic differential equations," Computational Statistics, Springer, vol. 32(4), pages 1357-1373, December.
    • Handle: RePEc:spr:compst:v:32:y:2017:i:4:d:10.1007_s00180-017-0763-x
    DOI: 10.1007/s00180-017-0763-x
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    References listed on IDEAS

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    1. Fang, Fang & Oosterlee, Kees, 2008. "A Novel Pricing Method For European Options Based On Fourier-Cosine Series Expansions," MPRA Paper 9319, University Library of Munich, Germany.
    2. Bouchard, Bruno & Touzi, Nizar, 2004. "Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 111(2), pages 175-206, June.
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