The binomial option pricing model: The trouble with dividends
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
We identify a problem in the widely used binomial option pricing model when it is used to value options on an asset paying continuous dividends. It does not value pairs of European spot and futures options consistently even though they are theoretically equivalent. The inconsistency arises from the way dividend yield is incorporated into the jumps and probabilities. In addition, the model also has the tendency to undervalue American options due to suboptimal early exercise decisions. While the lingering effect of this problem diminishes asymptotically, it is nonetheless a concern for someone just beginning to learn the model or in applications where the use of a sufficiently large binomial tree is not practical or economical. We propose a simple modification to solve the problem and demonstrate the effectiveness of the solution.
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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 | 0.000 | 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