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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

Author

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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

    as
    1. 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.
    2. Peter Carr & Robert Jarrow & Ravi Myneni, 1992. "Alternative Characterizations Of American Put Options," Mathematical Finance, Wiley Blackwell, pages 87-106.
    3. 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.
    4. Carr, Peter, 1998. "Randomization and the American Put," Review of Financial Studies, Society for Financial Studies, pages 597-626.
    5. Broadie, Mark & Detemple, Jerome, 1996. "American Option Valuation: New Bounds, Approximations, and a Comparison of Existing Methods," Review of Financial Studies, Society for Financial Studies, pages 1211-1250.
    6. 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..
    7. Ju, Nengjiu, 1998. "Pricing an American Option by Approximating Its Early Exercise Boundary as a Multipiece Exponential Function," Review of Financial Studies, Society for Financial Studies, 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, pages 263-276.
    9. S. D. Jacka, 1991. "Optimal Stopping and the American Put," Mathematical Finance, Wiley Blackwell, pages 1-14.
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