Bibliographic record
Abstract
An interesting and important question about options is how much they expand the range of investment opportunities in the market. In the Black-Scholes framework, the market is already “dynamically complete”: options are redundant assets because any option payoff can be replicated by dynamically trading the underlying asset and riskless bonds. But in the real world, options do expand investment opportunities, because the replication strategy entails infinite trading and infinite transaction costs. The next question is whether options can make the market statically complete, in that any possible contingency can be perfectly hedged by a static portfolio of options. Theory shows that this is true, but that it requires an infinite number of options with a continuum of different strikes. In this article, Cassano considers how close one can get to the ideal of static completeness using just a small number of options. Since not all risk can be hedged, how close is “close” depends on the investor’s utility function. But Cassano shows that under standard assumptions with risk aversion in a range that is commonly assumed, it only takes a handful of different options, say four or five, to achieve such near-completeness that it would only be worth a few pennies per hundred dollars of wealth to a typical investor to go the rest of the way to a fully complete market.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.044 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.006 |
| Scholarly communication | 0.007 | 0.034 |
| Open science | 0.001 | 0.004 |
| Research integrity | 0.005 | 0.004 |
| Insufficient payload (model declined to judge) | 0.016 | 0.003 |
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".