Strong order one convergence of a drift implicit Euler scheme: Application to the CIR process

Aurélien Alfonsi

doi:10.1016/j.spl.2012.10.034

Strong order one convergence of a drift implicit Euler scheme: Application to the CIR process

Aurélien Alfonsi

Research output: Contribution to journal › Article › peer-review

81 Citations (Scopus)

Abstract

We study the convergence of a drift implicit scheme for one-dimensional SDEs that was considered by Alfonsi (2005) for the Cox-Ingersoll-Ross (CIR) process. Under general conditions, we obtain a strong convergence of order1. In the CIR case, Dereich etal. (2012) have shown recently a strong convergence of order1 / 2 for this scheme. Here, we obtain a strong convergence of order1 under more restrictive assumptions on the CIR parameters.

Original language	English
Pages (from-to)	602-607
Number of pages	6
Journal	Statistics and Probability Letters
Volume	83
Issue number	2
DOIs	https://doi.org/10.1016/j.spl.2012.10.034
Publication status	Published - 1 Feb 2013

Keywords

Cox-Ingersoll-Ross model
Drift implicit Euler scheme
Lamperti transformation
Strong error

Access to Document

10.1016/j.spl.2012.10.034

Cite this

@article{972b2a93290043c3bd15442e20f7f34e,

title = "Strong order one convergence of a drift implicit Euler scheme: Application to the CIR process",

abstract = "We study the convergence of a drift implicit scheme for one-dimensional SDEs that was considered by Alfonsi (2005) for the Cox-Ingersoll-Ross (CIR) process. Under general conditions, we obtain a strong convergence of order1. In the CIR case, Dereich etal. (2012) have shown recently a strong convergence of order1 / 2 for this scheme. Here, we obtain a strong convergence of order1 under more restrictive assumptions on the CIR parameters.",

keywords = "Cox-Ingersoll-Ross model, Drift implicit Euler scheme, Lamperti transformation, Strong error",

author = "Aur{\'e}lien Alfonsi",

year = "2013",

month = feb,

day = "1",

doi = "10.1016/j.spl.2012.10.034",

language = "English",

volume = "83",

pages = "602--607",

journal = "Statistics and Probability Letters",

issn = "0167-7152",

publisher = "Elsevier B.V.",

number = "2",

}

TY - JOUR

T1 - Strong order one convergence of a drift implicit Euler scheme

T2 - Application to the CIR process

AU - Alfonsi, Aurélien

PY - 2013/2/1

Y1 - 2013/2/1

N2 - We study the convergence of a drift implicit scheme for one-dimensional SDEs that was considered by Alfonsi (2005) for the Cox-Ingersoll-Ross (CIR) process. Under general conditions, we obtain a strong convergence of order1. In the CIR case, Dereich etal. (2012) have shown recently a strong convergence of order1 / 2 for this scheme. Here, we obtain a strong convergence of order1 under more restrictive assumptions on the CIR parameters.

AB - We study the convergence of a drift implicit scheme for one-dimensional SDEs that was considered by Alfonsi (2005) for the Cox-Ingersoll-Ross (CIR) process. Under general conditions, we obtain a strong convergence of order1. In the CIR case, Dereich etal. (2012) have shown recently a strong convergence of order1 / 2 for this scheme. Here, we obtain a strong convergence of order1 under more restrictive assumptions on the CIR parameters.

KW - Cox-Ingersoll-Ross model

KW - Drift implicit Euler scheme

KW - Lamperti transformation

KW - Strong error

U2 - 10.1016/j.spl.2012.10.034

DO - 10.1016/j.spl.2012.10.034

M3 - Article

AN - SCOPUS:84870691951

SN - 0167-7152

VL - 83

SP - 602

EP - 607

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

IS - 2

ER -

Strong order one convergence of a drift implicit Euler scheme: Application to the CIR process

Abstract

Keywords

Access to Document

Fingerprint

Cite this