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On the valuation of constant barrier options under spectrally one-sided exponential Lévy models and Carr's approximation for American puts

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  • Avram, Florin
  • Chan, Terence
  • Usabel, Miguel

Abstract

This paper provides a general framework for pricing options with a constant barrier under spectrally one-sided exponential Lévy model, and uses it to implement of Carr's approximation for the value of the American put under this model. Simple analytic approximations for the exercise boundary and option value are obtained.

Suggested Citation

  • Avram, Florin & Chan, Terence & Usabel, Miguel, 0. "On the valuation of constant barrier options under spectrally one-sided exponential Lévy models and Carr's approximation for American puts," Stochastic Processes and their Applications, Elsevier, vol. 100(1-2), pages 75-107, July.
    • Handle: RePEc:eee:spapps:v:100:y::i:1-2:p:75-107
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    References listed on IDEAS

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    1. Carr, Peter, 1998. "Randomization and the American Put," The Review of Financial Studies, Society for Financial Studies, vol. 11(3), pages 597-626.
    2. Neil Shephard & Ole E. Barndorff-Nielsen, 2000. "Modelling by Levy Processes for Financial Econometrics," Economics Series Working Papers 2000-W03, University of Oxford, Department of Economics.
    3. Peter Carr & Robert Jarrow & Ravi Myneni, 2008. "Alternative Characterizations Of American Put Options," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 5, pages 85-103, World Scientific Publishing Co. Pte. Ltd..
    4. Zhang, Xiaolan, 1995. "Formules quasi-explicites pour les options américaines dans un modèle de diffusion avec sauts," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 38(1), pages 151-161.
    5. Broadie, Mark & Detemple, Jerome, 1996. "American Option Valuation: New Bounds, Approximations, and a Comparison of Existing Methods," The Review of Financial Studies, Society for Financial Studies, vol. 9(4), pages 1211-1250.
    6. Xiao Lan Zhang, 1997. "Numerical Analysis of American Option Pricing in a Jump-Diffusion Model," Mathematics of Operations Research, INFORMS, vol. 22(3), pages 668-690, August.
    7. Ju, Nengjiu, 1998. "Pricing an American Option by Approximating Its Early Exercise Boundary as a Multipiece Exponential Function," The Review of Financial Studies, Society for Financial Studies, vol. 11(3), pages 627-646.
    8. Gerber, Hans U. & Landry, Bruno, 1998. "On the discounted penalty at ruin in a jump-diffusion and the perpetual put option," Insurance: Mathematics and Economics, Elsevier, vol. 22(3), pages 263-276, July.
    9. S. D. Jacka, 1991. "Optimal Stopping and the American Put," Mathematical Finance, Wiley Blackwell, vol. 1(2), pages 1-14, April.
    10. Hans Gerber & Elias Shiu, 1998. "Pricing Perpetual Options for Jump Processes," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(3), pages 101-107.
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    Citations

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    Cited by:

    1. Jean-Philippe Aguilar, 2021. "The value of power-related options under spectrally negative Lévy processes," Review of Derivatives Research, Springer, vol. 24(2), pages 173-196, July.
    2. 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.
    3. Pistorius, M. R., 2003. "On doubly reflected completely asymmetric Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 107(1), pages 131-143, September.
    4. Tim Siu-Tang Leung & Kazutoshi Yamazaki, 2010. "American Step-Up and Step-Down Default Swaps under Levy Models," Papers 1012.3234, arXiv.org, revised Sep 2012.
    5. Aleksandar Mijatovic & Martijn Pistorius & Johannes Stolte, 2014. "Randomisation and recursion methods for mixed-exponential Levy models, with financial applications," Papers 1410.7316, arXiv.org.
    6. Svetlana Boyarchenko & Sergei Levendorskii, 2005. "American options: the EPV pricing model," Annals of Finance, Springer, vol. 1(3), pages 267-292, August.
    7. Lin, X. Sheldon & Wang, Tao, 2009. "Pricing perpetual American catastrophe put options: A penalty function approach," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 287-295, April.
    8. Oleg Kudryavtsev & Sergei Levendorskiǐ, 2009. "Fast and accurate pricing of barrier options under Lévy processes," Finance and Stochastics, Springer, vol. 13(4), pages 531-562, September.
    9. Jean-Philippe Aguilar, 2019. "The value of power-related options under spectrally negative L\'evy processes," Papers 1910.07971, arXiv.org, revised Jan 2021.
    10. Asmussen, Søren & Avram, Florin & Pistorius, Martijn R., 2004. "Russian and American put options under exponential phase-type Lévy models," Stochastic Processes and their Applications, Elsevier, vol. 109(1), pages 79-111, January.
    11. Ning Cai & S. G. Kou, 2011. "Option Pricing Under a Mixed-Exponential Jump Diffusion Model," Management Science, INFORMS, vol. 57(11), pages 2067-2081, November.
    12. Jorge Gonz'alez C'azares & Aleksandar Mijatovi'c, 2020. "Simulation of the drawdown and its duration in L\'{e}vy models via stick-breaking Gaussian approximation," Papers 2011.06618, arXiv.org, revised Mar 2021.

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