Work

Recursive algorithm for transition density approximation and simulation of diffusion processes

Year: 2025

Type: article

Abstract: ABSTRACT Diffusion processes and more generally, stochastic differential equations (SDEs), are widely used to model natural and financial systems. However, accurately simulating them remains challenging due to the limitations of discretization methods. We propose a recursive algorithm to approximate the transition density of scalar diffusion processes using Hermite polynomial expansions. Unlike standard numerical schemes, our method uses an expansion in Hermite polynomials to approximate the transition density without requiring an arbitrarily small discretization step. This approximation is then used to simulate diffusion paths with high fidelity. Numerical experiments, including the Vasicek and CIR processes, confirm the effectiveness and efficiency of the method.

Source: Statistica Neerlandica

DOI: 10.1111/stan.70020

Authors: Samir Ben‐Hariz, Youssef Esstafa, Helmi Zaatra

Institutions: Le Mans Université, Laboratoire Manceau de Mathématiques, Qatar University

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: hybrid

Estimated APC paid: $3,800

Funders: Le Mans Université, Agence Nationale de la Recherche, Institut Louis Bachelier, Conseil Régional des Pays de la Loire