A DISCRETE–TIME APPROACH TO ARBITRAGE-FREE PRICING OF CREDIT DERIVATIVES
Bibliographic record
Abstract
1 Wewould like to thank Dan Chen, Louis Gagnon and participants in seminars at the Kansas City Federal Reserve and the Credit Risk Conference, Toronto, for their comments. We are especially grateful to two referees for their detailed suggestions on improving the paper's presentation and content. Although it will not evidence runtime errors, the program code presented in this paper is intended only as pseudo-code. Usage of the code is permitted with proper attribution, at the user's risk. This paper develops a framework for modelling risky debt and valuing credit derivatives that is exible and simple to implement, and that is, to the maximum extent possible, based on observables. Our approach is based on expanding the Heath-Jarrow-Morton term-structure model to allow for defaultable debt. We do not follow the procedure of implying out the behavior of spreads from assumptions concerning the default process, instead working directly with the evolution of spreads. We show that risk-neutral drifts in the resulting model possess a recursive representation that particularly facilitates implementation and makes it possible to handle path-dependence and early exercise features without di culty. The framework permits embedding a variety of speci cations for default; we present an empirical example of a default structure which provides promising calibration results. 1
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.012 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".