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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

Limit behavior of the prices of a barrier option in the Black-Scholes model with random drift and volatility


Authors: Yu. S. Mishura and Yu. V. Yukhnovs’kii
Translated by: N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 84 (2011).
Journal: Theor. Probability and Math. Statist. 84 (2012), 99-106
MSC (2010): Primary 60G44, 60F05, 60B12
Published electronically: July 31, 2012
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Abstract: A generalized Black-Scholes model with random drift and volatility dependent on a parameter is studied in the paper. Sufficient conditions for the convergence of a sequence of prices of a European barrier option are established.


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Additional Information

Yu. S. Mishura
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 4E, Kiev 03127, Ukraine
Email: myus{@}univ.kiev.ua

Yu. V. Yukhnovs’kii
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 4E, Kiev 03127, Ukraine
Email: Yuhnovskiy{@}hq.eximb.com

DOI: http://dx.doi.org/10.1090/S0094-9000-2012-00863-6
PII: S 0094-9000(2012)00863-6
Keywords: Stochastic integrals, functional limit theorems, weak convergence, semimartingales, barrier options
Received by editor(s): January 10, 2011
Published electronically: July 31, 2012
Article copyright: © Copyright 2012 American Mathematical Society