CDO valuation: term structure, tranche structure, and loss distributions, working paper
Bibliographic record
Abstract
the Institute Laue-Langevin, where some of this work was carried out, for their hospitality; and Julien Houdain and Fortis Investments for providing the market prices used in the examples of this article. 4The support of the Natural Sciences and Engineering Research Council of Canada is acknowledged. This article describes a new approach to the risk-neutral valuation of CDO tranches, based on a general specification of the loss distribution, and the expected loss at zero default, for the reference portfolio. The new approach can describe tranche term-structures, and the generality with which the basic distributions are specified allows it to be perfectly calibrated to any set of market prices (for any number of tranches and maturities) that is arbitrage-free. Also, given a set of arbitrage-free market prices, arbitrage-free interpolated term structures (plots of tranche price versus maturity for a given tranche) and tranche structures (plots of tranche price versus tranche for a given maturity), as well as implied loss distributions, can be obtained, allowing bespoke tranches to be priced. The marking to market of tranche prices, and the establishment of forward-start premiums for the index are discussed. An efficient linear programming approach to valuation, essential to the implementation, is also described. The article also makes use of a new, simple yet general, approach to the problem of unequal notionals, and of random, time-dependent, risk-neutral, recovery rates.
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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 | 0.015 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.004 | 0.007 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.007 | 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 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".