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An Alternative Formula to Price American Options

Author

Listed:
  • Rocío Elizondo
  • Pablo Padilla
  • Mogens Bladt

Abstract

We give a new way to price American options, using Samuelson´s formula. We first obtain the option price corresponding to a European option at time t, weighting it by the probability that the underlying asset takes the value S at time t. This factor is given by the solution of the Fokker-Planck (Kolmogorov) equation for the transition probability density. The main advantage of this approach is that we can introduce systematically the effect of macroeconomic factors. If a macroeconomic framework is given by a dynamic system in the form of a set of ordinary differential equations we only have to solve a partial differential equation, for the transition probability density. In this context, we verify, for the sake of consistency, that this formula is consistent with the Black-Scholes model.

Suggested Citation

  • Rocío Elizondo & Pablo Padilla & Mogens Bladt, 2009. "An Alternative Formula to Price American Options," Working Papers 2009-06, Banco de México.
  • Handle: RePEc:bdm:wpaper:2009-06
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    File URL: http://www.banxico.org.mx/publicaciones-y-discursos/publicaciones/documentos-de-investigacion/banxico/%7BF98179CF-D9C5-9B47-1BB9-EE032F102577%7D.pdf
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    References listed on IDEAS

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    1. Bladt, Mogens & Rydberg, Tina Hviid, 1998. "An actuarial approach to option pricing under the physical measure and without market assumptions," Insurance: Mathematics and Economics, Elsevier, vol. 22(1), pages 65-73, May.
    2. Sergei Levendorskii, 2004. "The American put and European options near expiry, under Levy processes," Papers cond-mat/0404103, arXiv.org.
    3. Rocío Elizondo & Pablo Padilla, 2008. "An Analytical Approach to Merton’s Rational Option Pricing Theory," Working Papers 2008-03, Banco de México.
    4. Robert A. Jarrow, 1988. "Preferences, Continuity, and the Arbitrage Pricing Theory," Review of Financial Studies, Society for Financial Studies, vol. 1(2), pages 159-172.
    5. Francesc Llerena-Garrés, 2000. "Una nota sobre valoración de opciones americanas y arbitraje," Investigaciones Economicas, Fundación SEPI, vol. 24(1), pages 207-218, January.
    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. 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, vol. 9(4), pages 1211-1250.
    8. Geske, Robert & Johnson, Herb E, 1984. " The American Put Option Valued Analytically," Journal of Finance, American Finance Association, vol. 39(5), pages 1511-1524, December.
    9. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    American options; Fokker-Planck; Black-Scholes; Samuelson; density probability function.;

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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