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An Analytical Approach to Merton's Rational Option Pricing Theory

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  • Elizondo Rocío
  • Padilla Pablo

Abstract

In the early 70's Merton developed a theory based on economic arguments to study the properties of option and warrant prices. The main tool in his proofs was the portafolio dominance principle. In the context where the prices of a contingent claim satisfies a partial differential equation we provide analytical proofs of Merton's rational option pricing theory. We use several versions of the maximum principle as well as the sliding and the moving planes methods to prove our results. Our approach enables us to extend the theory to nonlinear models.

Suggested Citation

  • Elizondo Rocío & Padilla Pablo, 2008. "An Analytical Approach to Merton's Rational Option Pricing Theory," Working Papers 2008-03, Banco de México.
    • Handle: RePEc:bdm:wpaper:2008-03
    as

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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Francesc Llerena-Garrés, 2000. "Una nota sobre valoración de opciones americanas y arbitraje," Investigaciones Economicas, Fundación SEPI, vol. 24(1), pages 207-218, January.
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    Cited by:

    1. Elizondo Rocío & Padilla Pablo & Bladt Mogens, 2009. "An Alternative Formula to Price American Options," Working Papers 2009-06, Banco de México.

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    More about this item

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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