The Black-Scholes Currency Option Pricing Model: Evidence for Unbiasedness from Three Currencies against the US Dollar
Bibliographic record
Abstract
Under risk neutrality and rational expectations, the future value of the option premium is an unbiased estimator of the future actual payoff of the option. In this paper, this unbiasedness hypothesis is tested for the Black-Scholes currency call option pricing model. Three currencies, against the US dollar, are considered: the British pound, the Swiss franc, and the Japanese yen. The data is monthly and starts from the late 1980s. A set of seven different strike prices are assumed for each currency. Unbiasedness is supported if the regression constants are statistically insignificant, and if the regression slopes are statistically insignificantly different from 1, and if there is no autocorrelation in the regression residuals. The results for the British pound are strongly supportive of this version of market option efficiency. For the other two currencies only long run cointegration relations are uncovered. The results, whether short run or long run, remain also strongly supportive when the theoretical constraints are imposed. In addition, the results are not materially different with alternative measures of currency volatility. It can be concluded that the Black-Scholes currency option pricing model is relevant not only theoretically but also empirically and practically.
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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 | 0.020 | 0.059 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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".