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Alternative Randomization For Valuing American Options

Author

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  • TOSHIKAZU KIMURA

    (Graduate School of Economics and Business Administration, Hokkaido University, Kita 9, Nishi 7, Kita-ku, Sapporo 060-0809, Japan)

Abstract

This paper deals with randomization methods for valuing American options written on dividend-paying assets, which are based on the idea of treating the maturity date as a random variable. In the randomization method introduced by Carr in 1998, he used the Erlangian distributed random variable to develop a recursive algorithm starting from the so-called Canadian option with an exponentially distributed random maturity. The purposes of this paper are (i) to provide much simpler pricing formulas for the Canadian option; (ii) to interpret the Gaver–Stehfest method developed for inverting Laplace transforms as an alternative randomization method in the context of valuing American options; and (iii) to evaluate the performance of the Gaver–Stehfest method in details with theoretical and numerical views. Numerical experiments indicate that the Gaver–Stehfest method works well to generate accurate approximations for the early exercise boundary as well as the option value.

Suggested Citation

  • Toshikazu Kimura, 2010. "Alternative Randomization For Valuing American Options," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 27(02), pages 167-187.
    • Handle: RePEc:wsi:apjorx:v:27:y:2010:i:02:n:s0217595910002624
    DOI: 10.1142/S0217595910002624
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    References listed on IDEAS

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    1. Peter Carr, 1996. "Valuing Finite-Lived Options as Perpetual," Finance 9607002, University Library of Munich, Germany.
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    Cited by:

    1. Leippold, Markus & Vasiljević, Nikola, 2017. "Pricing and disentanglement of American puts in the hyper-exponential jump-diffusion model," Journal of Banking & Finance, Elsevier, vol. 77(C), pages 78-94.
    2. Walter Farkas & Ludovic Mathys & Nikola Vasiljevi'c, 2020. "Intra-Horizon Expected Shortfall and Risk Structure in Models with Jumps," Papers 2002.04675, arXiv.org, revised Jan 2021.
    3. Yuanda Chen & Zailei Cheng & Haixu Wang, 2023. "Option Pricing for the Variance Gamma Model: A New Perspective," Papers 2306.10659, arXiv.org.
    4. Walter Farkas & Ludovic Mathys, 2020. "Geometric Step Options with Jumps. Parity Relations, PIDEs, and Semi-Analytical Pricing," Papers 2002.09911, arXiv.org.
    5. Walter Farkas & Ludovic Mathys & Nikola Vasiljević, 2021. "Intra‐Horizon expected shortfall and risk structure in models with jumps," Mathematical Finance, Wiley Blackwell, vol. 31(2), pages 772-823, April.

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