Pricing of New Securities in an Incomplete Market: the Catch 22 of No‐Arbitrage Pricing
Bibliographic record
Abstract
There are two distinctly different approaches to the valuation of a new security in an incomplete market. The first approach takes the prices of the existing securities as fixed and uses no‐arbitrage arguments to derive the set of equivalent martingale measures that are consistent with the initial prices of the traded securities. The price of the new security is then obtained by appealing to certain criteria or on the basis of some preference assumption. The second method prices the new security within a general equilibrium framework. This paper clarifies the distinction between the two approaches and provides a simple proof that the introduction of the new security will typically change the prices of all the existing securities. We are left with the paradox that a genuinely new derivative security is not redundant, but the dominant pricing paradigm in derivative security pricing is the no‐arbitrage approach, which requires the redundancy of the security. Given the widespread practice of using the no‐arbitrage approach to price (or bound the price of) a new security, we also comment on some justifications for this approach.
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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 | 0.005 | 0.022 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.013 |
| Scholarly communication | 0.006 | 0.025 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.004 | 0.007 |
| Insufficient payload (model declined to judge) | 0.004 | 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".