An Analytical Approach to Merton’s Rational Option Pricing Theory
AbstractIn 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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Bibliographic InfoPaper provided by Banco de México in its series Working Papers with number 2008-03.
Date of creation: Mar 2008
Date of revision:
Merton; rational theory; option pricing; Black-Scholes; maximum principle;
Find related papers by 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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- Francesc Llerena-Garrés, 2000. "Una nota sobre valoración de opciones americanas y arbitraje," Investigaciones Economicas, Fundación SEPI, vol. 24(1), pages 207-218, January.
- 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.
- 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.
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