Regime-switching affine term structures

TL;DR

This paper introduces a regime-switching affine term structure model for forward rates influenced by a Markov chain, providing explicit solutions and an algorithm for consistent forward curve modeling, with applications to interest rate and energy markets.

Contribution

It develops a tractable affine HJM framework with explicit solutions for regime-switching forward rate models, applicable to interest rate and energy markets.

Findings

Explicit solutions for regime-switching forward curves

An algorithm for consistent forward curve modeling

Numerical examples demonstrating model applicability

Abstract

We consider an HJM model setting for Markov-chain modulated forward rates. The underlying Markov chain is assumed to induce regime switches on the forward curve dynamics. Our primary focus is on the interest rate and energy futures markets. After deriving HJM-drift conditions for the two markets, we prove under the assumption of affine structure for the term structure that the forward curves are solutions to specific systems of ODEs that can be solved explicitly in many cases. This allows for a tractable model setting, and we present an algorithm for obtaining consistent forward curve models within our framework. We conclude by presenting some simple numerical examples.