A fast and enhanced shallow learning framework for solving free boundary options pricing problems
Bibliographic record
Abstract
<title>Abstract</title> We consider various non-standard and non-linear free boundary options pricing problems comprising the non-linear free boundary local volatility model, exotic options, and dividend-paying pricing model and present a fast and enhanced shallow learning framework for solving free boundary options pricing problems with auxiliary neural operators (ANOs). To this end, we first rigorously explore the efficacy of some featured activation functions (FAFs) for solving these models with ANOs. We observe that some existing and ad-hoc activation functions perform well, but are not suitable for generalization. Rather, they should be enhanced to be adaptable to specific model characteristics and conditions based on their positivity, boundedness, convexity, vanishing points, discontinuous points, exploding points, etc. By adapting some of the existing activation functions and accustoming new ones, we then obtain a fast and enhanced shallow learning method which substantially improve the performance of neural network methodologies for non-standard options pricing models.
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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 | 0.002 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.003 |
| 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".