Regime-switching affine term structures

Paper: arXiv 2302.07721

Authors: Andreas Celary, Paul Eisenberg, Zehra Eksi

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.

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous mathematical framework extending HJM term structure models to regime-switching environments for interest rates and energy futures using systems of ODEs. However, it focuses heavily on theoretical derivations and offers only simple numerical examples rather than robust empirical backtesting or real-data validation.

Research Flowchart

  flowchart TD
    A[Goal: Tractable Regime-Switching HJM Forward Rate Model] --> B[Inputs: Markov-Chain State Dynamics & Initial Curves]
    B --> C[Derive HJM-Drift Conditions for Rates & Energy Futures]
    C --> D[Apply Affine Term Structure Assumption]
    D --> E[Solve Resulting Explicit Systems of ODEs]
    E --> F[Algorithm for Consistent Forward Curve Calibration]
    F --> G[Outcome: Analytical Tractability & Numerical Examples]