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

DOI:
https://doi.org/10.1090/tpms/987

Published electronically:
August 10, 2016

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 , where 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