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A simple and efficient numerical method for pricing discretely monitored early-exercise options

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  • Min Huang
  • Guo Luo

Abstract

We present a simple, fast, and accurate method for pricing a variety of discretely monitored options in the Black-Scholes framework, including autocallable structured products, single and double barrier options, and Bermudan options. The method is based on a quadrature technique, and it employs only elementary calculations and a fixed one-dimensional uniform grid. The convergence rate is $O(1/N^4)$ and the complexity is $O(MN\log N)$, where $N$ is the number of grid points and $M$ is the number of observation dates.

Suggested Citation

  • Min Huang & Guo Luo, 2019. "A simple and efficient numerical method for pricing discretely monitored early-exercise options," Papers 1905.13407, arXiv.org, revised Jun 2019.
    • Handle: RePEc:arx:papers:1905.13407
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    References listed on IDEAS

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    1. C. F. Lo & H. C. Lee & C. H. Hui, 2003. "A simple approach for pricing barrier options with time-dependent parameters," Quantitative Finance, Taylor & Francis Journals, vol. 3(2), pages 98-107.
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    4. Lord, Roger & Fang, Fang & Bervoets, Frank & Oosterlee, Kees, 2007. "A fast and accurate FFT-based method for pricing early-exercise options under Lévy processes," MPRA Paper 1952, University Library of Munich, Germany.
    5. Gianluca Fusai & I. Abrahams & Carlo Sgarra, 2006. "An exact analytical solution for discrete barrier options," Finance and Stochastics, Springer, vol. 10(1), pages 1-26, January.
    6. Tristan Guillaume, 2015. "Autocallable Structured Products," Post-Print hal-02979985, HAL.
    7. Alfredo Ibáñez & Carlos Velasco, 2018. "The optimal method for pricing Bermudan options by simulation," Mathematical Finance, Wiley Blackwell, vol. 28(4), pages 1143-1180, October.
    8. Tristan Guillaume, 2015. "Analytical Valuation of Autocallable Notes," Post-Print hal-02979983, HAL.
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    10. Liming Feng & Vadim Linetsky, 2008. "Pricing Discretely Monitored Barrier Options And Defaultable Bonds In Lévy Process Models: A Fast Hilbert Transform Approach," Mathematical Finance, Wiley Blackwell, vol. 18(3), pages 337-384, July.
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    13. Christian P. Fries & Mark S. Joshi, 2011. "Perturbation Stable Conditional Analytic Monte-Carlo Pricing Scheme For Auto-Callable Products," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(02), pages 197-219.
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    Cited by:

    1. Lyu, Jisang & Park, Eunchae & Kim, Sangkwon & Lee, Wonjin & Lee, Chaeyoung & Yoon, Sungha & Park, Jintae & Kim, Junseok, 2021. "Optimal non-uniform finite difference grids for the Black–Scholes equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 690-704.

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