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Perpetual American options

In: Non-Gaussian Merton-Black-Scholes Theory

Author

Listed:
  • Svetlana I. Boyarchenko

    (University of Texas at Austin, USA)

  • Sergei Z. Levendorskiĭ

    (Rostov State University of Economics, Russia)

Abstract

The following sections are included:The reduction to a free boundary problem for the stationary generalized Black-Scholes equationGeneral discussionFree boundary value problem for the price of the perpetual American optionMain LemmaPerpetual American put: the optimal exercise price and the rational put priceMain TheoremProof of optimality in the class $\mathcal{M}_0$Proof of optimality in the class $\mathcal{M}$Failure of the smooth pasting principle for some RLPE's and its substituteApproximate formulas for the case of model RLPEProof of Theorem 5.2Perpetual American callMain resultsProof of optimality in the case of unbounded payoffsPut-like and call-like options: the case of more general payoffsPut-like optionsCall-like optionsCommentary

Suggested Citation

  • Svetlana I. Boyarchenko & Sergei Z. Levendorskiĭ, 2002. "Perpetual American options," World Scientific Book Chapters, in: Non-Gaussian Merton-Black-Scholes Theory, chapter 5, pages 121-149, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789812777485_0005
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    Cited by:

    1. Yu-Ting Chen & Cheng Few Lee & Yuan-Chung Sheu, 2020. "An ODE Approach for the Expected Discounted Penalty at Ruin in a Jump-Diffusion Model," World Scientific Book Chapters, in: Cheng Few Lee & John C Lee (ed.), HANDBOOK OF FINANCIAL ECONOMETRICS, MATHEMATICS, STATISTICS, AND MACHINE LEARNING, chapter 41, pages 1561-1598, World Scientific Publishing Co. Pte. Ltd..
    2. Svetlana Boyarchenko & Sergei Levendorski&icaron;, 2007. "Practical Guide To Real Options In Discrete Time," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(1), pages 311-342, February.
    3. Luis Alvarez & Teppo Rakkolainen, 2010. "Investment timing in presence of downside risk: a certainty equivalent characterization," Annals of Finance, Springer, vol. 6(3), pages 317-333, July.
    4. Sergei Levendorskii, 2002. "Pseudo-diffusions and Quadratic term structure models," Papers cond-mat/0212249, arXiv.org, revised Apr 2004.

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