Direct Solution of Black-Scholes-Merton European Put Option Model on Dividend Yield With Modified-Log Payoff Function
Bibliographic record
Abstract
This paper proposes a framework based on the celebrated transform of Mellin type (MT) for the direct solution of the Black-Scholes-Merton European Put Option Model (BSMEPOM) on Dividend Yield (DY) with Modified-Log Payoff Function (MLPF) under the geometric Brownian motion. The focal goal of this paper is to use MT to obtain a valuation formula for the European Put Option (EPO) which pays a DY with MLPF. By means of the MT and its inversion formula, the price of EPO on DY was expressed in terms of integral equation. The valuation formula of EPO was obtained with the help of the convolution property of MT and final time condition. MT was tested on an illustrative example in order to measure its performance, effectiveness and suitability. The MLPF was compared with other existing payoff functions. Hence, the effect of DY on the pricing of EPO with MLPF was also investigated.
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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 | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| 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".