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The weak convergence of Greek symbols for prices of European options: from discrete time to continuous


Authors: S. V. Kuchuk-Iatsenko and Yu. S. Mishura
Translated by: S. Kvasko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 91 (2014).
Journal: Theor. Probability and Math. Statist. 91 (2015), 93-104
MSC (2010): Primary 91G20, 60F10, 60J67
DOI: https://doi.org/10.1090/tpms/969
Published electronically: February 4, 2016
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Abstract: The behavior of the so-called ``Greeks'' that characterize the financial market and assets on it for the Black-Scholes model is investigated in this paper. Discrete analogues of these quantities are introduced for the binomial model. The weak convergence of these analogues to the Greeks in the Black-Scholes model is established under the condition that the number of periods tends to infinity.


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Additional Information

S. V. Kuchuk-Iatsenko
Affiliation: Department of Integral and Differential Equations, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue, 6, Kyiv 03127, Ukraine
Email: kuchuk.iatsenko@gmail.com

Yu. S. Mishura
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue, 6, Kyiv 03127, Ukraine
Email: myus@univ.kiev.ua

DOI: https://doi.org/10.1090/tpms/969
Keywords: Greek symbols (``Greeks''), Black--Scholes model, binomial model, local de Moivre--Laplace theorem
Received by editor(s): October 1, 2014
Published electronically: February 4, 2016
Article copyright: © Copyright 2016 American Mathematical Society