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An Analytical Approach to Merton’s Rational Option Pricing Theory

Author

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  • Rocío Elizondo
  • Pablo Padilla

Abstract

In the early 70s 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 portfolio dominance principle. In the context where the price 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

  • Rocío Elizondo & Pablo Padilla, 2008. "An Analytical Approach to Merton’s Rational Option Pricing Theory," Working Papers 2008-03, Banco de México.
  • Handle: RePEc:bdm:wpaper:2008-03
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    File URL: http://www.banxico.org.mx/publicaciones-y-discursos/publicaciones/documentos-de-investigacion/banxico/%7B480D9F85-2B38-E743-14B7-B6FCB9A36A2C%7D.pdf
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    References listed on IDEAS

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

    More about this item

    Keywords

    Merton; rational theory; option pricing; Black-Scholes; maximum principle;

    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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