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.
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

research
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...
research
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...
research
06/29/2023

Efficient Sobolev approximation of linear parabolic PDEs in high dimensions

In this paper, we study the error in first order Sobolev norm in the app...
research
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...
research
12/29/2019

Convergence of the Two Point Flux Approximation and a novel fitted Two-Point Flux Approximation method for pricing options

In this paper, we deal with numerical approximations for solving the Bla...
research
06/28/2021

Continuous data assimilation and long-time accuracy in a C^0 interior penalty method for the Cahn-Hilliard equation

We propose a numerical approximation method for the Cahn-Hilliard equati...
research
07/01/2018

A polynomial time log barrier method for problems with nonconvex constraints

Interior point methods (IPMs) that handle nonconvex constraints such as ...

Please sign up or login with your details

Forgot password? Click here to reset