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
Journal:
Theor. Probability and Math. Statist. 79 (2009), 171-178
MSC (2000):
Primary 91B28; Secondary 60G50, 60F05
DOI:
https://doi.org/10.1090/S0094-9000-09-00789-3
Published electronically:
December 30, 2009
MathSciNet review:
2494546
Full-text PDF Free Access
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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.
References
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References
- M. Broadie, P. Glasserman, and S. G. Kou, A continuity correction for discrete barrier options, Math. Finance 7 (1997), 325–349. MR 1482707 (99k:90023)
- M. Broadie, P. Glasserman, and S. G. Kou, Connecting discrete and continuous path-dependent options, Finance Stoch. 3 (1999), 55–82. MR 1805321 (2001k:91066)
- P. Carmona, F. Petit, J. Pitman, and M. Yor, On the law of homogeneous functionals of the Brownian bridge, Studia Sci. Math. Hungar. 35 (1999), 445–455. MR 1762255 (2001f:60080)
- E. Csáki, A. Földes, and P. Salminen, On the joint distribution of the maximum and its location for a linear diffusion, Ann. Inst. H. Poincaré Probab. Statist. 23 (1987), 179–194. MR 891709 (88k:60145)
- P. Hörfelt, Extension of the corrected barrier approximation by Broadie, Glasserman, and Kou, Finance Stoch. 7 (2003), 231–243. MR 1968947 (2004b:91102)
- P. E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations, Springer, Berlin, 1992. MR 1214374 (94b:60069)
- S. G. Kou, On pricing of discrete barrier options, Statist. Sinica 13 (2003), 955–964. MR 2026057 (2005a:62225)
- R. C. Merton, Theory of rational option pricing, Bell J. Econom. and Management Sci. 4 (1973), 141–183. MR 0496534 (58:15058)
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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
Received by editor(s):
March 7, 2008
Published electronically:
December 30, 2009
Article copyright:
© Copyright 2009
American Mathematical Society
