A Study of Variance Reduction Techniques for American Option Pricing
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Bibliographic record
Abstract
American option pricing is a challenging problem in financial mathematics for which several approaches have been proposed in the last few years. In this paper, we consider the regression-based method of Longstaff and Schwartz (2001) to price these options, and then investigate the use of different variance reduction techniques to improve the efficiency of the Monte Carlo estimators thus obtained. The techniques considered have been shown to work well for European option pricing. One of them is importance sampling, in which the approach of Glasserman, Heidelberger, and Shahabuddin (1999) is applied to find an appropriate change of measure. We also consider control variates and randomized quasiMonte Carlo methods, and use numerical experiments on American Asian call options to investigate the performance of these methods.
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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 | 0.000 | 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 | 0.000 |
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