Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Monte Carlo Methods and Applications

Managing Editor: Sabelfeld, Karl K.

Editorial Board: Binder, Kurt / Bouleau, Nicolas / Chorin, Alexandre J. / Dimov, Ivan / Dubus, Alain / Egorov, Alexander D. / Ermakov, Sergei M. / Halton, John H. / Heinrich, Stefan / Kalos, Malvin H. / Lepingle, D. / Makarov, Roman / Mascagni, Michael / Mathe, Peter / Niederreiter, Harald / Platen, Eckhard / Sawford, Brian R. / Schmid, Wolfgang Ch. / Schoenmakers, John / Simonov, Nikolai A. / Sobol, Ilya M. / Spanier, Jerry / Talay, Denis

4 Issues per year


CiteScore 2016: 0.70

SCImago Journal Rank (SJR) 2016: 0.647
Source Normalized Impact per Paper (SNIP) 2016: 0.908

Mathematical Citation Quotient (MCQ) 2016: 0.33

Online
ISSN
1569-3961
See all formats and pricing
More options …
Volume 11, Issue 4

Issues

On the discretization schemes for the CIR (and Bessel squared) processes

Aurélien Alfonsi
  • CERMICS, projet MATHFI, Ecole Nationale des Ponts et Chaussées, 6-8 avenue Blaise Pascal, Cité Descartes, Champs sur Marne, 77455 Marne-la-vallée, France
  • e-mail :
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar

In this paper, we focus on the simulation of the Cox-Ingersoll-Ross processes and present several discretization schemes of both the implicit and explicit types. We study their strong and weak convergence. We also examine numerically their behaviour and compare them to the schemes already proposed by Deelstra and Delbaen and Diop. Finally, we gather all the results obtained and recommend, in the standard case, the use of one of our explicit schemes.

Key Words: simulation,; discretization scheme,; squared Bessel process,; Cox-Ingersoll-Ross model,; Romberg method.

About the article

Published Online:

Published in Print: 2005-12-01


Citation Information: Monte Carlo Methods and Applications mcma, Volume 11, Issue 4, Pages 355–384, ISSN (Online) 1569-3961, ISSN (Print) 0929-9629, DOI: https://doi.org/10.1515/156939605777438569.

Export Citation

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[2]
Vigirdas Mackevičius and Gabrielė Mongirdaitė
Modern Stochastics: Theory and Applications, 2018, Volume 5, Number 1, Page 113
[3]
Frederic von Wegner, Helmut Laufs, and Enzo Tagliazucchi
Physical Review E, 2018, Volume 97, Number 2
[4]
Grigori N. Milstein and John Schoenmakers
Advances in Applied Probability, 2015, Volume 47, Number 04, Page 1132
[5]
Andrei Cozma, Matthieu Mariapragassam, and Christoph Reisinger
SIAM Journal on Financial Mathematics, 2018, Volume 9, Number 1, Page 127
[6]
Yuji Shinozaki
SIAM Journal on Financial Mathematics, 2017, Volume 8, Number 1, Page 901
[7]
Mario Hefter and André Herzwurm
Journal of Mathematical Analysis and Applications, 2017
[8]
Mátyás Barczy, Mohamed Ben Alaya, Ahmed Kebaier, and Gyula Pap
Stochastic Processes and their Applications, 2017
[10]
Chao Zheng
SIAM Journal on Numerical Analysis, 2017, Volume 55, Number 3, Page 1243
[11]
Jianguo Tan, Hua Yang, Weiwei Men, and Yongfeng Guo
Journal of Computational and Applied Mathematics, 2017, Volume 320, Page 96
[12]
Martin Altmayer and Andreas Neuenkirch
IMA Journal of Numerical Analysis, 2017, Page drw063
[13]
Grigori N. Milstein and John Schoenmakers
Advances in Applied Probability, 2016, Volume 48, Number 04, Page 1095
[14]
Jean-François Chassagneux, Antoine Jacquier, and Ivo Mihaylov
SIAM Journal on Financial Mathematics, 2016, Volume 7, Number 1, Page 993
[15]
Christoph Reisinger and Andrei Cozma
Discrete and Continuous Dynamical Systems - Series B, 2016, Volume 21, Number 10, Page 3359
[16]
Edward Allen
Discrete and Continuous Dynamical Systems - Series B, 2016, Volume 21, Number 7, Page 2073
[17]
Xu Yang and Xiaojie Wang
Numerical Algorithms, 2017, Volume 74, Number 1, Page 39
[19]
Grigori N. Milstein and John Schoenmakers
Advances in Applied Probability, 2015, Volume 47, Number 04, Page 1132
[20]
Antanas Lenkšas and Vigirdas Mackevičius
Lithuanian Mathematical Journal, 2015, Volume 55, Number 4, Page 555
[21]
Mireille Bossy, Olivier Faugeras, and Denis Talay
The Journal of Mathematical Neuroscience (JMN), 2015, Volume 5, Number 1
[22]
Timothee Papin and Gabriel Turinici
Global Credit Review, 2015, Volume 05, Number 01, Page 19
[23]
C. Dion and V. Genon-Catalot
Statistical Inference for Stochastic Processes, 2016, Volume 19, Number 2, Page 131
[24]
A. Lenkšas and V. Mackevičius
Mathematics and Computers in Simulation, 2015, Volume 113, Page 1
[25]
Vigirdas Mackevičius
Lithuanian Mathematical Journal, 2015, Volume 55, Number 1, Page 119
[26]
Martin Altmayer and Andreas Neuenkirch
SIAM Journal on Financial Mathematics, 2015, Volume 6, Number 1, Page 22
[27]
T. Pellegrino and P. Sabino
Quantitative Finance, 2015, Volume 15, Number 5, Page 761
[28]
TIMOTHEE PAPIN and GABRIEL TURINICI
International Journal of Theoretical and Applied Finance, 2014, Volume 17, Number 04, Page 1450028
[29]
G.M. Leonenko and T.N. Phillips
Journal of Computational and Applied Mathematics, 2015, Volume 273, Page 296
[30]
Andreas Neuenkirch and Lukasz Szpruch
Numerische Mathematik, 2014, Volume 128, Number 1, Page 103
[31]
Kay Giesecke and Dmitry Smelov
Operations Research, 2013, Volume 61, Number 4, Page 894
[32]
Nan Chen and Zhengyu Huang
Mathematics of Operations Research, 2013, Volume 38, Number 3, Page 591
[33]
SIMON J. A. MALHAM and ANKE WIESE
International Journal of Theoretical and Applied Finance, 2013, Volume 16, Number 03, Page 1350014
[34]
Timothee Papin and Gabriel Turinici
Abstract and Applied Analysis, 2013, Volume 2013, Page 1
[35]
Xianming Sun and Siqing Gan
Computational Economics, 2014, Volume 43, Number 4, Page 433
[36]
Nadia Belaribi, François Cuvelier, and Francesco Russo
Stochastic Partial Differential Equations: Analysis and Computations, 2013, Volume 1, Number 1, Page 3
[37]
Moussa Kounta and Mario Lefebvre
Journal of Difference Equations and Applications, 2013, Volume 19, Number 8, Page 1276
[38]
Aurélien Alfonsi
Statistics & Probability Letters, 2013, Volume 83, Number 2, Page 602
[39]
Nikolaos Halidias
International Journal of Computer Mathematics, 2012, Volume 89, Number 6, Page 780
[40]
S. Dereich, A. Neuenkirch, and L. Szpruch
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2012, Volume 468, Number 2140, Page 1105
[41]
Vigirdas Mackevičius
Mathematics and Computers in Simulation, 2010, Volume 80, Number 5, Page 959
[42]
Saswati Dana and Soumyendu Raha
Journal of Computational Physics, 2011, Volume 230, Number 24, Page 8813
[43]
Vigirdas Mackevičius
Lithuanian Mathematical Journal, 2011, Volume 51, Number 3, Page 385
[44]
William T. Shaw and Asad Munir
The European Journal of Finance, 2009, Volume 15, Number 7-8, Page 661
[45]
E. Benhamou, E. Gobet, and M. Miri
SIAM Journal on Financial Mathematics, 2010, Volume 1, Number 1, Page 289
[46]
István Gyöngy and Miklós Rásonyi
Stochastic Processes and their Applications, 2011, Volume 121, Number 10, Page 2189
[47]
Roger Lord, Remmert Koekkoek, and Dick Van Dijk
Quantitative Finance, 2010, Volume 10, Number 2, Page 177
[48]
Graeme D. Chalmers and Desmond J. Higham
Journal of Difference Equations and Applications, 2010, Volume 16, Number 2-3, Page 143
[49]
Nicola Cufaro Petroni and Piergiacomo Sabino
Methodology and Computing in Applied Probability, 2013, Volume 15, Number 1, Page 147
[50]
Paul Glasserman and Kyoung-Kuk Kim
Finance and Stochastics, 2011, Volume 15, Number 2, Page 267
[51]
Abdel Berkaoui, Mireille Bossy, and Awa Diop
ESAIM: Probability and Statistics, 2008, Volume 12, Page 1
[52]
Piergiacomo Sabino
Computational Management Science, 2011, Volume 8, Number 1-2, Page 51
[53]
Mohamed El Makrini, Benjamin Jourdain, and Tony Lelièvre
ESAIM: Mathematical Modelling and Numerical Analysis, 2007, Volume 41, Number 2, Page 189
[54]
Lukasz Szpruch, Xuerong Mao, Desmond J. Higham, and Jiazhu Pan
BIT Numerical Mathematics, 2011, Volume 51, Number 2, Page 405
[55]
[56]
Mireille Bossy, Rajna Gibson, Francois-Serge Lhabitant, Nathalie Pistre, and Denis Talay
Review of Derivatives Research, 2007, Volume 9, Number 2, Page 109
[57]
Christian Kahl and Henri Schurz
Monte Carlo Methods and Applications, 2006, Volume 12, Number 2

Comments (0)

Please log in or register to comment.
Log in