Paper: arXiv 2401.11619

Authors: Claudio Fontana, Giacomo Lanaro, Agatha Murgoci

Abstract

We study the problems of consistency and of the existence of finite-dimensional realizations for multi-curve interest rate models of Heath-Jarrow-Morton type, generalizing the geometric approach developed by T. Björk and co-authors in the classical single-curve setting. We characterize when a multi-curve interest rate model is consistent with a given parameterized family of forward curves and spreads and when a model can be realized by a finite-dimensional state process. We illustrate the general theory in a number of model classes and examples, providing explicit constructions of finite-dimensional realizations. Based on these theoretical results, we perform the calibration of a three-curve Hull-White model to market data and analyse the stability of the estimated parameters.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 4.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous infinite-dimensional geometric framework to extend Björk’s finite-dimensional realization theory to multi-curve HJM models. While mathematically sophisticated and novel in its theoretical formulation, the empirical validation is limited to calibrating a specific three-curve Hull-White model, lacking extensive backtesting or deep data validation.

Research Flowchart

  flowchart TD
    A["Research Goal: Multi-Curve HJM Models<br/>(Consistency & Finite-Dimensional Realizations)"] --> B["Geometric Framework Setup<br/>(Generalizing Björk's Single-Curve Approach)"]
    B --> C["Theoretical Characterization<br/>(Conditions for FDR & Parameterized Family Consistency)"]
    C --> D["Model Classes & Examples<br/>(Explicit Constructions of FDRs)"]
    E["Market Data Inputs<br/>(Multi-Curve Forward Rates & Spreads)"] --> F["Empirical Calibration<br/>(Three-Curve Hull-White Model)"]
    D --> F
    F --> G["Key Outcomes:<br/>Theoretical FDR Characterization &<br/>Calibrated Hull-White Parameter Stability"]