Initial Value Problem and Solution for Dynamic Term Structure with Predictable Risk Free Interest Rate
Bibliographic record
Abstract
The initial condition for dynamic term structure modeling should be set before bond maturity when information about the state of economy is still available. If the state vector follows mean-reverting Gaussian Diffusion process, the solution is affine in the state vector and the risk-free interest rate is long rate. The existence of a non-stochastic or predictable risk-free interest rate has been a critical premise in financial economics. In equity and equity option pricing, since default-free bonds are assumed as risk-free assets, the risk-free interest rate may be approximated by the observable yields of short-term Treasury bills. If the dynamics of the entire term structure cannot be ignored, since none of the observable yields is risk-free, the risk-free interest rate must be an unobservable yet predictable common return on all riskless bond portfolios, which should be identifiable by a dynamic term structure model. However, the existing dynamic term structure models have all asserted the risk-free return on riskless bond portfolios as the stochastic instantaneous spot rate. The existence of a predictable risk-free interest rate has never been empirically verified because it has been precluded. Consider for simplicity that dynamic bond pricing is a function of a single latent state factor, P ( x, t, T). By the arbitrage argument of Black and Scholes (1973), Harrison and Kreps (1979), Harrison and Pliska (1981), among others, since the bond pricing risk from the state factor can be eliminated by forming a portfolio of a pair of bonds with different maturities, the portfolio should earn an instantaneously risk-free return R (t), which should be constant or predictable. Hence, the arbitrage-free bond price process is governed by a fundamental partial differential equation (PDE):
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How this classification was reachedexpand
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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".