Pricing and Hedging with Discontinuous Functions: Quasi–Monte Carlo Methods and Dimension Reduction
Why this work is in the frame
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Bibliographic record
Abstract
Quasi–Monte Carlo (QMC) methods are important numerical tools in the pricing and hedging of complex financial instruments. The effectiveness of QMC methods crucially depends on the discontinuity and the dimension of the problem. This paper shows how the two fundamental limitations can be overcome in some cases. We first study how path-generation methods (PGMs) affect the structure of the discontinuities and what the effect of discontinuities is on the accuracy of QMC methods. The insight is that the discontinuities can be QMC friendly (i.e., aligned with the coordinate axes) or not, depending on the PGM. The PGMs that offer the best performance in QMC methods are those that make the discontinuities QMC friendly. The structure of discontinuities can affect the accuracy of QMC methods more significantly than the effective dimension. This insight motivates us to propose a novel way of handling the discontinuities. The basic idea is to align the discontinuities with the coordinate axes by a judicious design of a method for simulating the underlying processes. Numerical experiments demonstrate that the proposed method leads to dramatic variance reduction in QMC methods for pricing options and for estimating Greeks. It also reduces the effective dimension of the problem. This paper was accepted by Assaf Zeevi, stochastic models and simulation.
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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 | 0.002 | 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 | 0.001 |
| 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