Pricing Asian and Barrier Options Using a Combined Heston Model and Monte Carlo Simulation Approach with Artificial Intelligence
Bibliographic record
Abstract
The computation of fair values for exotic options often necessitates complex pricing techniques, which remain sparsely addressed in academic literature. Predominantly, the assessment of fair value for vanilla options relies on methodologies such as the Black-Scholes model or Monte Carlo simulations. This study proposes an innovative, dynamic approach to pricing, leveraging artificial intelligence in conjunction with the Heston model and a Monte Carlo simulation engine. This approach aims to furnish estimates of the prices for Barrier and Asian options. To enhance the accuracy of the model, calibration was performed employing a supervised machine learning algorithm, a continuous risk-free curve, and a dynamic implied volatility surface, derived from the current market data of vanilla options on S&P 500 futures. The amalgamation of these models yields instantaneous pricing for exotic option derivatives, contingent on the investor's determination of time to maturity and barrier levels. The efficacy of the model was evaluated by comparing the output prices to theoretical model predictions and a selection of over-the-counter traded options. Our findings indicate that the proposed dynamic, integrated approach substantially reduces the disparity between the theoretical models and current market prices. The prices calculated by our model demonstrate a marginal error of merely 0.33% in comparison to market prices, a significant improvement over the considerably larger error of 3.12% exhibited by traditional 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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| 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 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".