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), 171178
MSC (2000):
Primary 91B28; Secondary 60G50, 60F05
Published electronically:
December 30, 2009
MathSciNet review:
2494546
Fulltext PDF Free Access
Abstract 
References 
Similar Articles 
Additional Information
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 BlackScholes 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.
 1.
Mark
Broadie, Paul
Glasserman, and Steven
Kou, A continuity correction for discrete barrier options,
Math. Finance 7 (1997), no. 4, 325–349. MR 1482707
(99k:90023), http://dx.doi.org/10.1111/14679965.00035
 2.
Mark
Broadie, Paul
Glasserman, and S.
G. Kou, Connecting discrete and continuous pathdependent
options, Finance Stoch. 3 (1999), no. 1,
55–82. MR
1805321 (2001k:91066), http://dx.doi.org/10.1007/s007800050052
 3.
P.
Carmona, F.
Petit, J.
Pitman, and M.
Yor, On the laws of homogeneous functionals of the Brownian
bridge, Studia Sci. Math. Hungar. 35 (1999),
no. 34, 445–455. MR 1762255
(2001f:60080)
 4.
Endre
Csáki, Antónia
Földes, and Paavo
Salminen, On the joint distribution of the maximum and its location
for a linear diffusion, Ann. Inst. H. Poincaré Probab. Statist.
23 (1987), no. 2, 179–194 (English, with French
summary). MR
891709 (88k:60145)
 5.
Per
Hörfelt, Extension of the corrected barrier approximation by
Broadie, Glasserman, and Kou, Finance Stoch. 7
(2003), no. 2, 231–243. MR 1968947
(2004b:91102), http://dx.doi.org/10.1007/s007800200077
 6.
Peter
E. Kloeden and Eckhard
Platen, Numerical solution of stochastic differential
equations, Applications of Mathematics (New York), vol. 23,
SpringerVerlag, Berlin, 1992. MR 1214374
(94b:60069)
 7.
S.
G. Kou, On pricing of discrete barrier options, Statist.
Sinica 13 (2003), no. 4, 955–964. Statistical
applications in financial econometrics. MR 2026057
(2005a:62225)
 8.
Robert
C. Merton, Theory of rational option pricing, Bell J. Econom.
and Management Sci. 4 (1973), 141–183. MR 0496534
(58 #15058)
 1.
 M. Broadie, P. Glasserman, and S. G. Kou, A continuity correction for discrete barrier options, Math. Finance 7 (1997), 325349. MR 1482707 (99k:90023)
 2.
 M. Broadie, P. Glasserman, and S. G. Kou, Connecting discrete and continuous pathdependent options, Finance Stoch. 3 (1999), 5582. MR 1805321 (2001k:91066)
 3.
 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), 445455. MR 1762255 (2001f:60080)
 4.
 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), 179194. MR 891709 (88k:60145)
 5.
 P. Hörfelt, Extension of the corrected barrier approximation by Broadie, Glasserman, and Kou, Finance Stoch. 7 (2003), 231243. MR 1968947 (2004b:91102)
 6.
 P. E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations, Springer, Berlin, 1992. MR 1214374 (94b:60069)
 7.
 S. G. Kou, On pricing of discrete barrier options, Statist. Sinica 13 (2003), 955964. MR 2026057 (2005a:62225)
 8.
 R. C. Merton, Theory of rational option pricing, Bell J. Econom. and Management Sci. 4 (1973), 141183. MR 0496534 (58:15058)
Similar Articles
Retrieve articles in Theory of Probability and Mathematical Statistics
with MSC (2000):
91B28,
60G50,
60F05
Retrieve articles in all journals
with MSC (2000):
91B28,
60G50,
60F05
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/S0094900009007893
PII:
S 00949000(09)007893
Received by editor(s):
March 7, 2008
Published electronically:
December 30, 2009
Article copyright:
© Copyright 2009
American Mathematical Society
