Extracting Model-Free Volatility from Option Prices
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Bibliographic record
Abstract
The CBOE9s VIX index is a measure of the implied volatility (IV) in 30-day stock index options. Originally constructed as a weighted average of Black-Scholes IVs from 8 at the money calls and puts, the VIX was redesigned in 2003. The new VIX uses a nonparametric procedure to extract an IV from out of the money calls and puts over the full range of strikes. Implementation of the theoretical procedure, however, requires several approximations, for example to deal with the fact that only a discrete set of strikes are traded in the market, rather than a continuum over the full range from zero to infinity, as required by the theory. In this article, Jiang and Tian look carefully at the new VIX algorithm to assess the impact of these approximations on its accuracy. They find that some of them may produce substantial errors, even in simply recovering the volatility input from a set of options in a pure Black-Scholes world. They then propose a modified calculation technique using a smoothing algorithm, that can almost entirely eliminate the errors. <b>TOPICS:</b>Options, statistical methods, risk management
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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 | 0.000 |
| 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 it