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Rate of convergence of option prices by using the method of pseudomoments


Authors: Yu. S. Mishura and E. Yu. Munchak
Translated by: N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 92 (2015).
Journal: Theor. Probability and Math. Statist. 92 (2016), 117-133
MSC (2010): Primary 60F15, 91B25, 91G20
Published electronically: August 10, 2016
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Abstract: A sequence of discrete time financial markets is considered in the scheme of series. The rate of convergence for put and call option prices in the discrete-time model is studied if the prices of risky assets weakly converge to those in the Black-Scholes model. This rate of convergence is of order $ O (n ^ {- 1}) $, where $ n $ is the number of trading periods on a fixed time interval for the prelimit model. The result follows from an author theorem concerning the rate of convergence in the central limit theorem for identically distributed random variables, and the latter is obtained by using the method of pseudomoments.


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Additional Information

Yu. S. Mishura
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, Volodymyrs’ka Street, 64/13, 01601, Kyiv, Ukraine
Email: myus@univ.kiev.ua

E. Yu. Munchak
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, Volodymyrs’ka Street, 64/13, 01601, Kyiv, Ukraine
Email: yevheniamunchak@gmail.com

DOI: https://doi.org/10.1090/tpms/987
Keywords: Financial markets in discrete and continuous time, scheme of series, pseudomoments, rate of convergence, option prices, Black--Scholes model
Received by editor(s): May 6, 2015
Published electronically: August 10, 2016
Article copyright: © Copyright 2016 American Mathematical Society