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American options: the EPV pricing model

Author

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  • Svetlana Boyarchenko

    (The University of Texas at Austin)

  • Sergei Levendorskii

    (The University of Texas at Austin)

Abstract

We explicitly solve the pricing problem for perpetual American puts and calls, and provide an efficient semi-explicit pricing procedure for options with finite time horizon. Contrary to the standard approach, which uses the price process as a primitive, we model the price process as the expected present value of a stream, which is a monotone function of a Levy process. Certain processes exhibiting mean-reverting, stochastic volatility and/or switching features can be modelled in this way. This specification allows us to consider assets that pay no dividends at all when the level of the underlying stochastic factor is too low, assets that pay dividends at a fixed rate when the underlying stochastic process remains in some range, or capped dividends.

Suggested Citation

  • Svetlana Boyarchenko & Sergei Levendorskii, 2004. "American options: the EPV pricing model," Finance 0405024, EconWPA.
  • Handle: RePEc:wpa:wuwpfi:0405024 Note: Type of Document - pdf; pages: 19
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    File URL: http://econwpa.repec.org/eps/fin/papers/0405/0405024.pdf
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    References listed on IDEAS

    as
    1. Hans U. Gerber & Hlias S. W. Shiu, 1996. "Martingale Approach To Pricing Perpetual American Options On Two Stocks," Mathematical Finance, Wiley Blackwell, vol. 6(3), pages 303-322.
    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. Bianca Hilberink & L.C.G. Rogers, 2002. "Optimal capital structure and endogenous default," Finance and Stochastics, Springer, vol. 6(2), pages 237-263.
    4. Svetlana Boyarchenko, 2004. "Irreversible Decisions and Record-Setting News Principles," American Economic Review, American Economic Association, vol. 94(3), pages 557-568, June.
    5. Chernov, Mikhail & Ronald Gallant, A. & Ghysels, Eric & Tauchen, George, 2003. "Alternative models for stock price dynamics," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 225-257.
    6. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
    7. Ole E. Barndorff-Nielsen, 1997. "Processes of normal inverse Gaussian type," Finance and Stochastics, Springer, vol. 2(1), pages 41-68.
    8. Bates, David S., 2003. "Empirical option pricing: a retrospection," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 387-404.
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    Citations

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    Cited by:

    1. Oscar Gutiérrez & Francisco Ruiz-Aliseda, 2011. "Real options with unknown-date events," Annals of Finance, Springer, vol. 7(2), pages 171-198, May.
    2. Boyarchenko, Svetlana & Levendorskii[caron], Sergei, 2007. "Optimal stopping made easy," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 201-217, February.
    3. Svetlana Boyarchenko & Sergei Levendorskii, 2005. "A theory of endogenous time preference, and discounted utility anomalies," Microeconomics 0506005, EconWPA.
    4. Boyarchenko Svetlana & Levendorskii Sergei Z, 2006. "General Option Exercise Rules, with Applications to Embedded Options and Monopolistic Expansion," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 6(1), pages 1-51, June.
    5. 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.
    6. Luis Alvarez & Teppo Rakkolainen, 2009. "Optimal payout policy in presence of downside risk," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(1), pages 27-58, March.
    7. repec:spr:compst:v:69:y:2009:i:1:p:27-58 is not listed on IDEAS
    8. Svetlana Boyarchenko & Sergei Levendorskii, 2005. "Discount factors ex post and ex ante, and discounted utility anomalies," Microeconomics 0510013, EconWPA, revised 13 Dec 2005.
    9. Christian Flor & Simon Hansen, 2013. "Technological advances and the decision to invest," Annals of Finance, Springer, vol. 9(3), pages 383-420, August.
    10. Kleinert, Florian & van Schaik, Kees, 2015. "A variation of the Canadisation algorithm for the pricing of American options driven by Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 125(8), pages 3234-3254.
    11. Boyarchenko, Svetlana & Levendorskii, Sergei, 2008. "Exit problems in regime-switching models," Journal of Mathematical Economics, Elsevier, vol. 44(2), pages 180-206, January.
    12. Boyarchenko, Svetlana & Levendorskii, Sergei, 2010. "Optimal stopping in Levy models, for non-monotone discontinuous payoffs," MPRA Paper 27999, University Library of Munich, Germany.
    13. Luis H. R. Alvarez & Teppo A. Rakkolainen, 2006. "A Class of Solvable Optimal Stopping Problems of Spectrally Negative Jump Diffusions," Discussion Papers 9, Aboa Centre for Economics.
    14. Florian Kleinert & Kees van Schaik, 2013. "A variation of the Canadisation algorithm for the pricing of American options driven by L\'evy processes," Papers 1304.4534, arXiv.org.

    More about this item

    Keywords

    Levy processes; option pricing; dividend paying assets.;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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