Variance Reduction for MC/QMC Methods to Evaluate Option Prices
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Bibliographic record
Abstract
AbstractSeveral variance reduction techniques including importance sampling, (martingale) control variate, (randomized) Quasi Monte Carlo method, QMC in short, and some possible combinations are considered to evaluate option prices. By means of perturbation methods to derive some option price approximations, we find from numerical results in Monte Carlo simulations that the control variate method is more efficient than importance sampling to solve European option pricing problems under multifactor stochastic volatility models. As an alternative, QMC method also provides better convergence than basic Monte Carlo method. But we find an example where QMC method may produce erroneous solutions when estimating the low-biased solution of an American option. This drawback can be effectively fixed by adding a martingale control to the estimator adopting Quasi random sequences so that low-biased estimates obtained are more accurate than results from Monte Carlo method. Therefore by taking advantages of martingale control variate and randomized QMC, we find significant improvement on variance reduction for pricing derivatives and their sensitivities. This effect should be understood as that martingale control variate plays the role of a smoother under QMC method to permit better convergence.
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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 | 0.003 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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