Sharp $L^1$-Approximation of the log-Heston SDE by Euler-type methods

Annalena Mickel; Andreas Neuenkirch

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arXiv · 2206.03229

Sharp $L^1$-Approximation of the log-Heston SDE by Euler-type methods

Annalena Mickel·Andreas Neuenkirch

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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.

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Annalena Mickel, Andreas Neuenkirch. 2023-04-25. Sharp $L^1$-Approximation of the log-Heston SDE by Euler-type methods. https://arxiv.org/abs/2206.03229

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