Bibliographic record
Abstract
Due to the properties of large transaction volumes, high innovation and positive promotion to the financial market development, options play an essential role. However, the flexible design of options leads to complicated pricing, which makes accurate option pricing a challenging task for a long time. In this paper, two types of neural networks - feed-forward networks such as the radial basis function (RBF), multilayer perceptron (MLP), Modular network and a recurrent deep learning network Long short-term memory (LSTM) - and three stochastic process pricing models (Black-Scholes-Merton model, Heston stochastic volatility model and Merton Jump-diffusion model) are proposed so as to predict European call option prices. Firstly, it generates simulated option prices data from three stochastic process models to test the effectiveness and approximation ability of the neural networks. Secondly, effective factors such as moneyness, time to maturity and greeks via the Black-Scholes-Merton formula are used as input variables for neural networks. Historical data of S&P 500 European option prices empirically analyzes validity and stability of the neural networks. The performance measures R2, statistical error of the root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE) are used to evaluate the performance of two types of pricing models. It shows that the MLP network with two hidden layers performs best. In addition, neural networks do outperform the pricing ability of stochastic process 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 | 0.007 | 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 | 0.002 | 0.001 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.003 | 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".