Empirical Insights into Interest Rate Dynamics Using the HJM Framework

Interest rates play a central role in shaping macroeconomic conditions, asset prices, and financial stability, yet accurately modeling their dynamics remains a persistent challenge. This paper presents a historical and empirical investigation of the Heath-Jarrow-Morton (HJM) framework, a no-arbitrage approach that models the entire forward-rate curve, using U.S. Treasury yield data. After reviewing the evolution of term-structure models, a one-factor HJM specification with an exponential volatility kernel is implemented and evaluated across multiple market regimes. Empirical results show that while the HJM framework effectively captures the central tendencies of yield curve movements, it systematically smooths extreme shifts during periods of financial stress, particularly at shorter maturities. To enhance economic interpretability, Ross's Recovery Theorem is applied conceptually to reinterpret risk-neutral dynamics as real-world probability measures, revealing that heightened uncertainty during crises is concentrated at medium and longer horizons. Additionally, machine-learning-based volatility estimation is explored as a hybrid extension to improve empirical responsiveness while preserving no-arbitrage consistency. Overall, the findings highlight both the strengths and structural limitations of classical HJM models and demonstrate how recovery theory and data-driven volatility estimation can meaningfully improve their explanatory power. The study contributes to bridging theoretical term-structure modeling with observed market behavior and investor expectations.