The weak convergence order of two Euler-type discretization schemes for the log-Heston model

Mickel, Annalena ; Neuenkirch, Andreas

Document Type: Article
Year of publication: 2023
The title of a journal, publication series: IMA Journal of Numerical Analysis : IMAJNA
Volume: tba
Issue number: tba
Page range: tba
Place of publication: Oxford
Publishing house: Oxford Univ. Press
ISSN: 0272-4979 , 1464-3642
Related URLs:
Publication language: English
Institution: School of Business Informatics and Mathematics > Wirtschaftsmathematik II (Neuenkirch 2013-)
Subject: 510 Mathematics
Abstract: We study the weak convergence order of two Euler-type discretizations of the log-Heston model where we use symmetrization and absorption, respectively, to prevent the discretization of the underlying CIR process from becoming negative. If the Feller index $\nu$ of the CIR process satisfies $\nu > 1$, we establish weak convergence order one, while for $\nu \leq 1, we obtain weak convergence order $\nu -\varepsilon$ for $\varepsilon > 0$ arbitrarily small. We illustrate our theoretical findings by several numerical examples.

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