Bibliographic record
Abstract
Abstract Although the Black–Scholes model lays the foundation to the modern option pricing theory, its empirical performance is rather unsatisfactory as manifested in the phenomenon known as volatility smile . This article explains what volatility smile is, and describes some nonparametric techniques and parametric models that may be used to deal with volatility smile for pricing and/or hedging purposes. Kernel regression and the GARCH option pricing model are chosen to be the nonparametric technique and parametric model, respectively, in our demonstration involving a sample of S&P 500 index options. Kernel regression is found to perform better than the GARCH model, but its applicability is limited to pricing the same type of options. Without providing a dynamic for the underlying asset price, kernel regression is also ill‐suited for hedging purposes. In contrast, the GARCH model is not subject to the same application limitations even though its performance on the same type of options is poorer. Thus, both nonparametric techniques and parametric models serve useful purposes in dealing with derivative contracts.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 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; both teacher heads agree on what is shown here.
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".