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

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.