Fuzzy Option Pricing Using a Novel Data-Driven Feed Forward Neural Network Volatility Model
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Bibliographic record
Abstract
Recently there has been a growing interest in combining randomness and fuzziness to solve option pricing problems in finance using volatility models such as GARCH (generalized autoregressive conditional heteroskedasticity) and Heston-Nandi GARCH. The possibility theory for fuzzy option pricing (for real option, European option and binary option) has been demonstrated in the literature by fuzzifying the parameters such as volatility. However, many fuzzy option pricing approaches remain difficult to use with real data. A neural network (NN) is a highly parameterized model, widely promoted as a universal approximator such that with enough data it could learn any smooth predictive relationship. In this paper we first introduce a novel data-driven feed forward NN predictive model for conditional variance and demonstrate the superiority of the proposed model for option pricing over other volatility models. Using the NN predictive model, two different fuzzy estimates of the sensitivity measure vega (ν, which measures the dependence of option price on volatility σ) are proposed. We use different estimates of the sensitivity measure and compute the α-cuts of the fuzzy call price.
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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 | 0.009 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.002 | 0.001 |
| 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