Extending the universality of the Heath–Jarrow–Morton model
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Bibliographic record
Abstract
Abstract Heath, Jarrow, and Morton (HJM) developed an important model of the evolution of interest rates. A key assumption of the model is that interest rate changes are normally distributed in continuous time. Implementing the HJM‐method of evolution of interest rates in discrete time for more complex volatility functions remains a significant challenge. In this article, we present a relatively simple and flexible method of implementation, that extends the usefulness of the HJM model. The derivation assumes that the distribution of interest rates is stable, but not necessarily identical, for each discrete time period. This allows us to identify the drift‐adjustment terms necessary to build interest rate lattices and trees and Monte Carlo simulations that satisfy exactly the no‐arbitrage and volatility conditions, even complex ones, of the model. The much more difficult discrete‐time implementation methods suggested in the literature (Heath, Jarrow, and Morton (1991) [Heath, D., Jarrow, R. & Morton, A. (1991). Contingent claim valuation with a random evolution of interest rates. Review of Futures Markets , 54–76.] and Jarrow (1996) [Jarrow, R. (1996). Modeling fixed income securities and interest rate options . New York, NY: McGraw‐Hill Companies Inc.]) do not accomplish that. We illustrate our analytical implementation with three examples of volatility functions and demonstrate its superiority to other methods of implementation.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it