On the speed of convergence of Piterbarg constants

TL;DR

This paper establishes an upper bound for the difference between continuous and discrete Piterbarg constants, enabling accurate approximation via Monte Carlo simulations with a known error rate.

Contribution

It provides a novel upper bound for the difference between continuous and discrete Piterbarg constants, facilitating their approximation.

Findings

Derived an explicit upper bound for the difference

Enabled approximation of Piterbarg constants using Monte Carlo

Provided an explicit error rate for the approximation

Abstract

In this paper we derive an upper bound for the difference between the continuous and discrete Piterbarg constants. Our result allows us to approximate the classical Piterbarg constants by their discrete counterparts using Monte Carlo simulations with an explicit error rate