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American options: the EPV pricing model

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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.

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File URL: http://128.118.178.162/eps/fin/papers/0405/0405024.pdf
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Bibliographic Info

Paper provided by EconWPA in its series Finance with number 0405024.

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Length: 19 pages
Date of creation: 18 May 2004
Date of revision:
Handle: RePEc:wpa:wuwpfi:0405024

Note: Type of Document - pdf; pages: 19
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Web page: http://128.118.178.162

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Keywords: Levy processes; option pricing; dividend paying assets.;

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References

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  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. Ole E. Barndorff-Nielsen, 1997. "Processes of normal inverse Gaussian type," Finance and Stochastics, Springer, vol. 2(1), pages 41-68.
  3. Sergey Levendorskiy & Svetlana Boyarchenko, 2004. "Practical guide to real options in discrete time," Computing in Economics and Finance 2004 137, Society for Computational Economics.
  4. Chernov, Mikhail & Gallant, A. Ronald & Ghysels, Eric & Tauchen, George, 2002. "Alternative Models for Stock Price Dynamic," Working Papers 02-03, Duke University, Department of Economics.
  5. 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.
  6. Bianca Hilberink & L.C.G. Rogers, 2002. "Optimal capital structure and endogenous default," Finance and Stochastics, Springer, vol. 6(2), pages 237-263.
  7. Bates, David S., 2003. "Empirical option pricing: a retrospection," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 387-404.
  8. Svetlana Boyarchenko, 2004. "Irreversible Decisions and Record-Setting News Principles," American Economic Review, American Economic Association, vol. 94(3), pages 557-568, June.
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Citations

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Cited by:
  1. Svetlana Boyarchenko & Sergey Levendorskiy, 2004. "Optimal stopping made easy," Finance 0410016, EconWPA.
  2. Luis H. R. Alvarez E. & Pekka Matom\"aki & Teppo A. Rakkolainen, 2013. "A Class of Solvable Optimal Stopping Problems of Spectrally Negative Jump Diffusions," Papers 1302.4181, arXiv.org.
  3. Christian Flor & Simon Hansen, 2013. "Technological advances and the decision to invest," Annals of Finance, Springer, vol. 9(3), pages 383-420, August.
  4. Luis Alvarez & Teppo Rakkolainen, 2009. "Optimal payout policy in presence of downside risk," Computational Statistics, Springer, vol. 69(1), pages 27-58, March.
  5. 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.
  6. Svetlana Boyarchenko & Sergei Levendorskii, 2005. "Discount factors ex post and ex ante, and discounted utility anomalies," Microeconomics 0510013, EconWPA, revised 17 Nov 2005.
  7. Oscar Gutierrez Arnaiz & Francisco Ruiz-Aliseda, 2003. "Real Options with Unknown-Date Events," Discussion Papers 1378, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  8. 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.
  9. Boyarchenko, Svetlana & Levendorskii, Sergei, 2010. "Optimal stopping in Levy models, for non-monotone discontinuous payoffs," MPRA Paper 27999, University Library of Munich, Germany.
  10. 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.
  11. Svetlana Boyarchenko & Sergei Levendorskii, 2005. "A theory of endogenous time preference, and discounted utility anomalies," Microeconomics 0506005, EconWPA.
  12. Boyarchenko, Svetlana & Levendorskii, Sergei, 2008. "Exit problems in regime-switching models," Journal of Mathematical Economics, Elsevier, vol. 44(2), pages 180-206, January.

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