Efficient estimation of one-dimensional diffusion first passage time densities via Monte Carlo simulation

TL;DR

This paper introduces a Monte Carlo simulation method for efficiently estimating the densities of first passage times in one-dimensional diffusions, achieving fast convergence and unbiasedness by leveraging exact simulation of Brownian bridges.

Contribution

The paper presents a novel Monte Carlo approach that directly estimates first passage time densities using Brownian bridge representations, improving accuracy and convergence speed.

Findings

Achieves almost unbiased density estimates

Convergence rate of 1/√N surpasses kernel smoothing methods

Method is computationally efficient and accurate

Abstract

We propose a method for estimating first passage time densities of one-dimensional diffusions via Monte Carlo simulation. Our approach involves a representation of the first passage time density as expectation of a functional of the three-dimensional Brownian bridge. As the latter process can be simulated exactly, our method leads to almost unbiased estimators. Furthermore, since the density is estimated directly, a convergence of order $1 / \sqrt{N}$, where $N$ is the sample size, is achieved, the last being in sharp contrast to the slower non-parametric rates achieved by kernel smoothing of cumulative distribution functions.