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

Abstract

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 $\nu \le 1$, we obtain weak convergence order $\nu -\epsilon$ for $\epsilon >0$ arbitrarily small. We illustrate our theoretical findings by several numerical examples.

Added refereces; corrected typos; revised Lemma 3.5, Proposition 3.6, Proposition 3.9 and the proof of Theorem 1.1, results unchanged