  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 $\nu-\epsilon$ for $\epsilon>0$ arbitrarily small. We
illustrate our theoretical findings by several numerical examples.
