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 ν of the CIR process satisfies ν>1, we establish weak convergence order $ 1 $, while for ν ≤ 1, we obtain weak convergence order ν -ε for ε>0 arbitrarily small. We illustrate our theoretical findings by several numerical examples.