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

 

On the rate of convergence of prices of barrier options with discrete and continuous time


Authors: O. M. Soloveyko and G. M. Shevchenko
Translated by: O. Klesov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 79 (2008).
Journal: Theor. Probability and Math. Statist. 79 (2009), 171-178
MSC (2000): Primary 91B28; Secondary 60G50, 60F05
Published electronically: December 30, 2009
MathSciNet review: 2494546
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Abstract: A barrier option is a derivative realized or cancelled if the price of the underlying asset crosses a certain barrier. Most of the models in financial mathematics are considered for markets with continuous time. However the trading days for a particular stock take place at separate moments, i.e. discretely. The Black-Scholes model is extended in the paper in the sense that we consider barrier options with varying drifts. We find the rate of convergence of prices of such options with discrete time to the prices of options with continuous time.


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Additional Information

O. M. Soloveyko
Affiliation: Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov avenue, 6, Kyiv 03127, Ukraine
Email: osoloveyko@univ.kiev.ua

G. M. Shevchenko
Affiliation: Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov avenue, 6, Kyiv 03127, Ukraine
Email: zhora@univ.kiev.ua

DOI: http://dx.doi.org/10.1090/S0094-9000-09-00789-3
PII: S 0094-9000(09)00789-3
Received by editor(s): March 7, 2008
Published electronically: December 30, 2009
Article copyright: © Copyright 2009 American Mathematical Society