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

TL;DR

This paper analyzes the weak convergence order of two Euler-type schemes for the log-Heston model, showing order one for certain parameters and near order for others, supported by numerical examples.

Contribution

It provides a detailed theoretical analysis of convergence orders for two discretization schemes of the log-Heston model based on the Feller index.

Findings

Order one convergence when Feller index > 1

Near order $ u- ext{epsilon}$ convergence when $ u \,\leq\, 1$

Numerical examples confirm theoretical results

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