From Stochastic Orders to Volatility Surfaces: Revisiting the One-X Property
Bibliographic record
Abstract
The One-X property, introduced by Zetocha in a 2023 paper, provides a novel stochastic order with direct implications for constructing arbitrage-free implied volatility surfaces. The current work revisits its theoretical foundations and explores its connections with classical stochastic orders, thereby offering a deeper understanding of its mathematical structure and practical significance in calendar-arbitrage-free modeling. We first present an explicit counterexample to a conjecture raised in Zetocha’s previous paper, and then provide a natural and valid enhancement of this conjecture. After discussing the inherent relations between the One-X property and properties such as TP2, RP2, and unimodality of density ratio (introcuded by Glasserman and Pirjol in their 2024 papers), we further explore some sufficient conditions to achieve the One-X property for random variables of certain mixture types that are frequently seen in applications.
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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 | 0.001 | 0.003 |
| 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".