CDO Models - Towards the Next Generation: Incomplete Markets and Term Structure
Bibliographic record
Abstract
This article describes a new approach to the risk-neutral valuation of CDO tranches, based on a general specification of the tranche loss distributions and the index default distribution. The new model is a term-structure model, 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. The use of the new model is illustrated by testing market prices for the standardized iTraxx index tranches (for all marketed tranches and maturities) to see if they are arbitrage-free. Other examples include the determination of the arbitrage-free range of prices allowed for an unmarketed standardized tranche and the determination of the cost of exiting a tranche position. For the latter example, both arbitrage-free price ranges, and a preferred price, are obtained. Prices for unmarketed maturities and unmarketed non-standard tranches are also obtained by an interpolation and extrapolation procedure. Because the model is an incomplete-market model characterized by many more parameters than market prices, it was essential to develop an efficient optimization approach to valuation. The article also makes use of a new approach to the problem of unequal recovery rates and notionals.
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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".