What the study found
The study proposes an unweighted function-space version of the Heath–Jarrow–Morton (HJM) framework for modeling the full yield curve, which is the set of interest rates across different maturities. The authors report that this setup can be calibrated to real-world yield data and can allow for negative interest rates.
Why the authors say this matters
The authors say the new setting avoids a drawback of earlier HJM implementations, where the choice of exponential weight cannot be estimated from market data and has no objective interpretation. They suggest the framework is useful for prediction and uncertainty quantification, and that it can handle the negative Euro bond yields observed in their sample.
What the researchers tested
The researchers discretized the HJM equation using a finite difference method and built a semiparametric model. They calibrated it on real-world yield data using a new functional principal component analysis-based approach, and they backtested and benchmarked it against a one-factor Vasicek model using historical data.
What worked and what didn't
The abstract says the proposed framework was calibrated on real-world yield data and used to illustrate simulation capabilities for prediction and uncertainty quantification. It also notes that, unlike widely studied U.S. treasuries, negative interest rates were observed for AAA Euro Bonds in the sample period, and the framework allows for negative yields.
What to keep in mind
The abstract does not provide detailed numerical results, performance metrics, or a full account of the backtesting outcomes. It also does not describe limitations beyond noting that earlier weighted function-space choices could not be estimated from market data.
Key points
- The paper introduces an unweighted function-space setting for the Heath–Jarrow–Morton framework.
- The authors say earlier exponentially weighted settings have weights that cannot be estimated from market data.
- The model was discretized with a finite difference approach and calibrated with a functional principal component analysis-based method.
- Backtesting and benchmarking were done against a one-factor Vasicek model.
- The sample included AAA Euro Bonds with negative interest rates, and the framework allows negative yields.
Disclosure
- Research title:
- Unweighted HJM framework allows negative yield modeling
- Authors:
- Michael Pokojovy, Ebenezer Nkum, Thomas M. Fullerton
- Institutions:
- Cigna (United States), Old Dominion University, The University of Texas at El Paso
- Publication date:
- 2026-03-11
- OpenAlex record:
- View
Get the weekly research newsletter
Stay current with scholarly research without reading academic papers — one filtered digest, every Friday.