Discretizing the Heston Model: An Analysis of the Weak Convergence Rate

TL;DR

This paper investigates the weak convergence rate of a discretization scheme for the Heston model, establishing a rate of order one under certain conditions and analyzing convergence without a rate under minimal assumptions, supported by numerical examples.

Contribution

It provides a rigorous analysis of the weak convergence rate for Heston model discretization, combining classical and modern techniques, which was previously not fully characterized.

Findings

Weak convergence rate of order one under mild assumptions.

Weak convergence without a rate under minimal assumptions.

Numerical examples validating theoretical results.

Abstract

In this manuscript we analyze the weak convergence rate of a discretization scheme for the Heston model. Under mild assumptions on the smoothness of the payoff and on the Feller index of the volatility process, respectively, we establish a weak convergence rate of order one. Moreover, under almost minimal assumptions we obtain weak convergence without a rate. These results are accompanied by several numerical examples. Our error analysis relies on a classical technique from Talay & Tubaro, a recent regularity estimate for the Heston PDE by Feehan & Pop and Malliavin calculus.