The Euler-Maruyama approximation for the absorption time of the CEV diffusion

TL;DR

This paper develops a weakly consistent Euler-Maruyama approximation method for the absorption time of the CEV diffusion process, addressing challenges in simulating hitting times where boundary non-degeneracy assumptions fail.

Contribution

It introduces a novel approximation scheme for absorption times of the CEV diffusion, overcoming limitations of existing methods that require boundary non-degeneracy.

Findings

The scheme provides a weakly consistent approximation for absorption times.

It extends simulation techniques to boundary cases where coefficients degenerate.

The approach is applicable to financial models involving CEV processes.

Abstract

A standard convergence analysis of the simulation schemes for the hitting times of diffusions typically requires non-degeneracy of their coefficients on the boundary, which excludes the possibility of absorption. In this paper we consider the CEV diffusion from the mathematical finance and show how a weakly consistent approximation for the absorption time can be constructed, using the Euler-Maruyama scheme.