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Valuing Finite-Lived Options as Perpetual

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  • Peter Carr

    (Morgan Stanley)

Abstract

We show how the value of a finite-lived option can be interpreted as the limit of a sequence of perpetual option values subject to default risk. This interpretation yields new closed form approximations for European and American option values in the Black Scholes model. Numerical results indicate that the approximation is both accurate and computationally efficient.

Suggested Citation

  • Peter Carr, 1996. "Valuing Finite-Lived Options as Perpetual," Finance 9607002, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpfi:9607002
    Note: Type of Document - Postscript - originally LaTeX; prepared on Unix - Tex; to print on Postscript; pages: 34; figures: included. We never published this piece and now we would like to reduce our mailing and xerox cost by posting it.
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    References listed on IDEAS

    as
    1. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    2. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    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..
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Dietmar P.J. Leisen, 1997. "The Random-Time Binomial Model," Finance 9711005, University Library of Munich, Germany, revised 29 Nov 1998.
    2. Chockalingam, Arun & Muthuraman, Kumar, 2015. "An approximate moving boundary method for American option pricing," European Journal of Operational Research, Elsevier, vol. 240(2), pages 431-438.
    3. Cristina Viegas & Jos� Azevedo-Pereira, 2012. "Mortgage valuation: a quasi-closed-form solution," Quantitative Finance, Taylor & Francis Journals, vol. 12(7), pages 993-1001, May.
    4. Mitya Boyarchenko & Sergei Levendorskiĭ, 2009. "Prices And Sensitivities Of Barrier And First-Touch Digital Options In Lévy-Driven Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(08), pages 1125-1170.
    5. Riccardo Fazio, 2015. "A Posteriori Error Estimator for a Front-Fixing Finite Difference Scheme for American Options," Papers 1504.04594, arXiv.org.
    6. Zhongkai Liu & Tao Pang, 2016. "An efficient grid lattice algorithm for pricing American-style options," International Journal of Financial Markets and Derivatives, Inderscience Enterprises Ltd, vol. 5(1), pages 36-55.
    7. 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.
    8. Cristina Viegas & José Azevedo-Pereira, 2020. "A Quasi-Closed-Form Solution for the Valuation of American Put Options," IJFS, MDPI, vol. 8(4), pages 1-16, October.
    9. Leisen, Dietmar P. J., 1999. "The random-time binomial model," Journal of Economic Dynamics and Control, Elsevier, vol. 23(9-10), pages 1355-1386, September.
    10. Leunglung Chan & Song-Ping Zhu, 2021. "An Analytic Approach for Pricing American Options with Regime Switching," JRFM, MDPI, vol. 14(5), pages 1-20, April.

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    More about this item

    Keywords

    American options; method of lines;

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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