Fourier space time-stepping for option pricing with Lévy models
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Bibliographic record
Abstract
Jump-diffusion and Lévy models have been widely used to partially alleviate some of the biases inherent in the classical Black–Scholes–Merton model. Unfortunately, the resulting pricing problem requires solving a more difficult partial integro-differential equation (PIDE), and although several approaches for solving the PIDE have been suggested in the literature, none are entirely satisfactory. We present an efficient algorithm, based on transform methods, which symmetrically treats the diffusive and integral terms, is applicable to a wide class of path-dependent options (such as Bermudan, American and barrier options) and options on multiple assets, and naturally extends to regime-switching Lévy models. Furthermore, we introduce a penalty method to improve the convergence of pricing American options.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| 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 it