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 <= 1, we obtain weak convergence order nu-? for ?> 0 arbitrarily small. We illustrate our theoretical findings by several numerical examples.