Pricing Multi-Asset Bermudan Commodity Options with Stochastic Volatility Using Neural Networks
Bibliographic record
Abstract
It has been recognized that volatility in commodity markets fluctuates significantly depending on the demand–supply relationship and geopolitical risk, and that risk and financial management using multivariate derivatives are becoming more important. This study illustrates an application of multi-layered neural networks for multi-dimensional Bermudan option pricing problems assuming a multi-asset stochastic volatility model in commodity markets. In addition, we aim to identify continuation value functions for these option pricing problems by implementing smooth activation functions in the neural networks and evaluating their accuracy compared with other activation functions or regression techniques. First, we express the underlying asset dynamics using the multi-asset stochastic volatility model with mean reversion properties in the commodity market and formulate the multivariate Bermudan commodity option pricing problem. Subsequently, we apply multi-layer perceptrons in the neural network to represent the continuation value functions of Bermudan commodity options, wherein the entire neural network is trained using the least-squares Monte Carlo simulation method. Finally, we perform numerical experiments and demonstrate that applications of neural networks for Bermudan options in a multi-dimensional commodity market achieve sufficient accuracy with regard to various aspects, including changing the exercise dates, the number of layers/neurons, and the dimension of the problem.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 source (direct Gemma or distilled Codex), 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".