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An Analytical Approach to Merton’s Rational Option Pricing Theory

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  • Rocío Elizondo
  • Pablo Padilla
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    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.

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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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    Bibliographic Info

    Paper provided by Banco de México in its series Working Papers with number 2008-03.

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    Date of creation: Mar 2008
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    Handle: RePEc:bdm:wpaper:2008-03

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    Web page: http://www.banxico.org.mx
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    Related research

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

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    1. 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.
    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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