On affine interest rate models

TL;DR

This paper explores the connection between Bernstein processes and affine interest rate models, revealing how symmetries in certain equations can describe these financial models.

Contribution

It establishes a novel link between Bernstein processes and one-factor affine interest rate models, enhancing understanding of their mathematical structure.

Findings

Bernstein processes relate to affine interest rate models

Symmetries of Hamilton-Jacobi-Bellman equations are key

New descriptions of interest rate models using Bernstein processes

Abstract

Bernstein processes are Brownian diffusions that appear in Euclidean Quantum Mechanics. Knowledge of the symmetries of the Hamilton-Jacobi-Bellman equation associated with these processes allows one to obtain relations between stochastic processes (Lescot-Zambrini, Progress in Probability, vols 58 and 59). More recently it has appeared that each one--factor affine interest rate model (in the sense of Leblanc-Scaillet) could be described using such a Bernstein process.