Local Refinement and Adaptive Strategy for a System of Free Boundary Power Options with High Order Compact Differencing
Bibliographic record
Abstract
In this research, we propose fourth-order non-uniform Hermitian differencing with a fifth-order adaptive time integration method for pricing system of free boundary exotic power put options consisting of the option value, delta sensitivity, and gamma. The main objective for implementing the above scheme is to carefully account for the irregularity in the locality of the left corner point after fixing the free boundary. Specifically and mainly, we stretch the performance of our proposed method threefold. First, we exploit the non-uniform fourth-order Hermitian scheme to locally concentrate space grid points arbitrarily close to the left boundary. Secondly, we further leverage the adaptive nature of the embedded time integration method, which allows optimal selection of a time step based on the space grid point distribution and regional variation. Thirdly, we introduce a fourth-order combined Hermitian scheme, which requires fewer grid points for computing the near boundary point of the delta sensitivity and gamma. Another novelty is how we approximate the optimal exercise boundary and its derivative using a fifth-order Robin boundary scheme and fourth-order combined Hermitian scheme. Our proposed method consistently achieves reasonable accuracy with very coarse grids and little runtime across the numerical experiments. We further compare the results with existing methods and the ones we obtained from the uniform space grid.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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 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".