Valuation of Convertible Bonds With Credit Risk
Bibliographic record
Abstract
Applying the technology of option pricing and contingent claims modeling to credit risk is one of the major growth areas in derivatives research these days. It is an old idea to treat default as a firm9s management rationally exercising the shareholders9 option to go bankrupt rather than to make a required payment to the debtholders. But only in the last few years has this insight been extended and widely applied to practical bond valuation problems. Convertible bonds have also become much more popular in recent years, as the weak and volatile stock market has combined with low interest rates to create an environment in which the conversion option can be very attractive. One critical uncertainty in credit risk analysis that may not be fully appreciated by those who have not worked in this area, is what the payoff to bondholders will actually be in the event of a default. In this article, Ayache, Forsyth, and Vetzal explore the interactions among the multiple options embedded in convertibles that are subject to default risk, call provisions, and put provisions, in addition to the conversion option. Along with results that illustrate the interactions among these multiple options, the authors provide a straightforward valuation technique for convertibles, by applying principles of linear complementarity to the discretization of the fundamental PDE of contingent claims pricing.
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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 | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".