Generalized control variate methods for pricing Asian options
Bibliographic record
Abstract
ABSTRACT The conventional control variate method proposed by Kemna and Vorst for evaluating Asian options using the Black-Scholes model utilizes a constant control parameter.We generalize this method, applying it to a stochastic control process through the martingale representation of the conventional control. This generalized control variate has zero variance in the optimal case, whereas the conventional control can only reduce its variance by a finite factor. By means of option price approximations, the generalized control is reduced to a linear martingale control. It is straightforward to extend this martingale control to a non-linear situation such as the American Asian option problem. From the variance analysis of martingales, the performance of control variate methods depends on the distance between the approximate martingale and the optimal martingale. This measure becomes helpful for the design of control variate methods for complex problems such as Asian options using stochastic volatility models.We demonstrate multiple choices of controls and test them with Monte Carlo and quasi-Monte Carlo simulations. Quasi-Monte Carlo methods perform significantly better after adding a control when using the two-step control variate method, while the variance reduction ratios increase to 320 times for randomized quasi-Monte Carlo methods, compared with 60 times for Monte Carlo simulations with a control.
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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 | 0.003 | 0.009 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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 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".