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On the convergence order of a binary tree approximation of symmetrized diffusion processes

Author

Listed:
  • Akahori, Jirô
  • Fan, Jie Yen
  • Imamura, Yuri

Abstract

The price of a barrier option is often computed numerically. Due to the path dependency, the convergence rate of such numerical approximation is generally of order 1/2. In this paper, we show that the convergence order can be achieved at 1 under certain condition. This confirms a numerical analysis done previously by the third author with others.

Suggested Citation

  • Akahori, Jirô & Fan, Jie Yen & Imamura, Yuri, 2023. "On the convergence order of a binary tree approximation of symmetrized diffusion processes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 211(C), pages 263-277.
    • Handle: RePEc:eee:matcom:v:211:y:2023:i:c:p:263-277
    DOI: 10.1016/j.matcom.2023.03.030
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    References listed on IDEAS

    as
    1. Gobet, Emmanuel, 2000. "Weak approximation of killed diffusion using Euler schemes," Stochastic Processes and their Applications, Elsevier, vol. 87(2), pages 167-197, June.
    2. Jirô Akahori & Yuri Imamura, 2014. "On a symmetrization of diffusion processes," Quantitative Finance, Taylor & Francis Journals, vol. 14(7), pages 1211-1216, July.
    3. Alexander Gairat & Vadim Shcherbakov, 2017. "Density Of Skew Brownian Motion And Its Functionals With Application In Finance," Mathematical Finance, Wiley Blackwell, vol. 27(4), pages 1069-1088, October.
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