Year: 2022
Type: preprint
Abstract: We study the $L^1$-approximation of the log-Heston SDE at equidistant time points by Euler-type methods. We establish the convergence order $ 1/2-ε$ for $ε>0$ arbitrarily small, if the Feller index $ν$ of the underlying CIR process satisfies $ν> 1$. Thus, we recover the standard convergence order of the Euler scheme for SDEs with globally Lipschitz coefficients. Moreover, we discuss the case $ν\leq 1$ and illustrate our findings by several numerical examples.
Source: arXiv (Cornell University)
Authors: Mickel, Annalena, Neuenkirch, Andreas
Institution: University of Mannheim
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
OpenAlex ID: W4281769266