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
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
MathSciNet review:
3364126
Full-text PDF Free Access
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Additional Information
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.
References
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References
- L.-B. Chang and K. Palmer, Smooth convergence in the Binomial model, Finance Stochastics 11 (2007), 91–105. MR 2284013 (2008f:62122)
- R. J. Elliott, Stochastic Calculus and Applications, Springer-Verlag, Berlin, 1982. MR 678919 (85b:60059)
- J. C. Cox, S. A. Ross, and M. Rubinstein, Option pricing: A simplified approach, J. Financial Economics 7 (1979), no. 3, 229–263.
- H. Föllmer and A. Schied, Stochastic Finance. An Introduction in Discrete Time, Second revised and extended edition, Studies in Mathematics, vol. 27, Walter de Gruyter, Berlin, 2004. MR 2169807 (2006d:91002)
- S. Heston and G. Zhou, On the rate of convergence of discrete-time contingent claims, Math. Finance 10 (2000), no. 1, 53–75. MR 1743973 (2000k:91053)
- C.-C. Hsia, On binomial option pricing, J. Financial Research 6 (1983), no. 1, 41–46.
- Y. Mishura, Diffusion approximation of recurrent schemes for financial markets, with application to Ornstein–Uhlenbeck process, Opuscula Math. 35 (2015), no. 1, 99–116. MR 3282967
- V. V. Petrov, Sums of Independent Random Variables, “Nauka”, Moscow, 1972; English transl, Springer-Verlag, Berlin, 1975. MR 0388499 (52:9335)
- V. P. Chistyakov, A Course in Probability Theory, “Nauka”, Moscow, 1982. (Russian) MR 695493 (84f:60001)
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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
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
