DeepAI AI Chat
Log In Sign Up

The order barrier for the L^1-approximation of the log-Heston SDE at a single point

12/14/2022
by   Annalena Mickel, et al.
University of Mannheim
0

We study the L^1-approximation of the log-Heston SDE at the terminal time point by arbitrary methods that use an equidistant discretization of the driving Brownian motion. We show that such methods can achieve at most order min{ν, 12}, where ν is the Feller index of the underlying CIR process. As a consequence Euler-type schemes are optimal for ν≥ 1, since they have convergence order 12-ϵ for ϵ >0 arbitrarily small in this regime.

READ FULL TEXT

page 1

page 2

page 3

page 4

06/21/2021

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...
06/07/2022

Sharp L^1-Approximation of the log-Heston SDE by Euler-type methods

We study the L^1-approximation of the log-Heston SDE at equidistant time...
11/09/2021

Optimal-order error estimates for Euler discretization of high-index saddle dynamics

High-index saddle dynamics provides an effective means to compute the an...
05/11/2021

Compact Euler Tours of Trees with Small Maximum Degree

We show how an Euler tour for a tree on n vertices with maximum degree d...
06/29/2022

Implicit and fully discrete approximation of the supercooled Stefan problem in the presence of blow-ups

We consider two implicit approximation schemes of the one-dimensional su...