<title>Parallel FFT approach for derivative pricing</title>
Bibliographic record
Abstract
Pricing of derivatives is one of the central problems in Computational Finance. Since the theory of derivative pricing is highly mathematical, numerical techniques such as lattice approach, finite-difference and finite-element techniques among others have been resorted in the past. Recently Fast Fourier Transform (FFT) have been used for such applications as derivative pricing. In the current work, we develop a parallel algorithm for FFT and implement it to price options. Our main aim is to study the performance of this algorithm. For a data size of N and P processors, a blocked data distribution for the algorithm in general produces log(N) - log(P) iterations of local communications and log(P) iterations of remote communications. Therefore, the algorithm is divided into two parts: local and remote. In the local algorithm, the processors perform the computations on their locally partitioned data elements without any communications. In the case of remote algorithm, the processors perform the computation on the local data elements with remote communications. In this paper we focus on the remote communication and computation aspect of the algorithm. We discuss the performance of our algorithm and the results (in general terms) from FFT algorithm and binomial tree algorithm developed and implemented for the same/similar problem. We make some general observation on these two algorithms.
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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 | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.018 | 0.006 |
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".