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An Alternative Formula to Price American Options

Author

Listed:
  • Elizondo Rocío
  • Padilla Pablo
  • Bladt Mogens

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 completeness, that this formula is consistent with the Black-Scholes model.

Suggested Citation

  • Elizondo Rocío & Padilla Pablo & Bladt Mogens, 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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    References listed on IDEAS

    as
    1. Sergei Levendorskii, 2004. "The American put and European options near expiry, under Levy processes," Papers cond-mat/0404103, arXiv.org.
    2. Robert A. Jarrow, 1988. "Preferences, Continuity, and the Arbitrage Pricing Theory," The Review of Financial Studies, Society for Financial Studies, vol. 1(2), pages 159-172.
    3. 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.
    4. 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.
    5. Elizondo Rocío & Padilla Pablo, 2008. "An Analytical Approach to Merton's Rational Option Pricing Theory," Working Papers 2008-03, Banco de México.
    6. Francesc Llerena-Garrés, 2000. "Una nota sobre valoración de opciones americanas y arbitraje," Investigaciones Economicas, Fundación SEPI, vol. 24(1), pages 207-218, January.
    7. 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..
    8. Broadie, Mark & Detemple, Jerome, 1996. "American Option Valuation: New Bounds, Approximations, and a Comparison of Existing Methods," The Review of Financial Studies, Society for Financial Studies, vol. 9(4), pages 1211-1250.
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    More about this item

    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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