Discretization error of Stochastic Integrals

TL;DR

This paper analyzes the asymptotic error distribution in stochastic integral approximation, develops optimal discretization schemes, and applies these to delta hedging and Euler-Maruyama methods.

Contribution

It introduces effective discretization schemes that minimize asymptotic mean-squared error and applies them to financial hedging and numerical approximation.

Findings

Discretization schemes attain lower bounds of error

Efficient delta hedging strategies are developed

Improved Euler-Maruyama approximation methods

Abstract

Asymptotic error distribution for approximation of a stochastic integral with respect to continuous semimartingale by Riemann sum with general stochastic partition is studied. Effective discretization schemes of which asymptotic conditional mean-squared error attains a lower bound are constructed. Two applications are given; efficient delta hedging strategies with transaction costs and effective discretization schemes for the Euler-Maruyama approximation are constructed.