Hamiltonian Flow Simulation of Rare Events

TL;DR

This paper presents a Hamiltonian Flow Monte Carlo method that efficiently estimates rare events and reduces variance in sampling, demonstrated through barrier option pricing.

Contribution

It introduces a novel HFMC algorithm that leverages Hamiltonian dynamics for improved rare event estimation and variance reduction over standard methods.

Findings

Variance reduction demonstrated compared to standard Monte Carlo.

Efficient sampling of rare events using Hamiltonian dynamics.

Successful application to barrier option pricing.

Abstract

Hamiltonian Flow Monte Carlo(HFMC) methods have been implemented in engineering, biology and chemistry. HFMC makes large gradient based steps to rapidly explore the state space. The application of the Hamiltonian dynamics allows to estimate rare events and sample from target distributions defined as the change of measures. The estimates demonstrated a variance reduction of the presented algorithm and its efficiency with respect to a standard Monte Carlo and interacting particle based system(IPS). We tested the algorithm on the case of the barrier option pricing.