Multigrid method for pricing European options under the CGMY process
Bibliographic record
Abstract
We propose a fast multigrid method for solving the discrete partial integro-differential equations (PIDEs) arising from pricing European options when the underlying asset is driven by an infinite activity Lévy process. We consider the CGMY model whose kernel singularity gets worse when the parameter <em>Y</em> approaches two. Due to the integral term, the discretization matrix is dense. In order to obtain an efficient multigrid method, we apply a fixed point iteration as a smoother for multigrid. In each smoothing step, we only need to solve a sparse matrix corresponding to the differential operator and compute a matrix-vector product involving the integral operator by a fast Fourier transform (FFT). We prove that the fixed point iteration smoother is effective reducing the high frequency components. Moreover, we also prove a two-grid convergence of the multigrid method by a local mode analysis. We demonstrate the effectiveness of the multigrid method by solving the option pricing equation under the CGMY model with finite and infinite variation processes.
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 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 | 0.001 | 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 | 0.001 |
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 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".