Accelerating Convergence in Trinomial Option Pricing: Recursive Incremental Value Ordering with Repeated Richardson Extrapolation
Bibliographic record
Abstract
The Black-Scholes model, widely utilized for option pricing, has evolved into a trinomial model approach, providing an alternative means for determining option prices.Nonetheless, the trinomial model faces limitations in terms of time efficiency and accuracy.This study explores the acceleration of the trinomial option prices' convergence and computation time reduction using repeated Richardson extrapolation (RRE), achieved by recursively determining the order of incremental values.Comparative analysis with other extrapolation methods revealed that the RRE technique outperforms the Aitken Neville method by approximately 11%.Applied to a case study involving technology and energy stock option pricing, this technique minimized the required time steps to an average of 0.04 seconds, simultaneously achieving a mean square error (MSE) value of 0.835 compared to the Black-Scholes value.Consequently, the proposed methodology offers potential enhancements in computational efficiency for financial applications employing nested discrete-time models.
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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 | 0.002 | 0.007 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".