The Importance of Estimating Implied Volatility Functions Using the Relevant Loss Function
Bibliographic record
Abstract
We investigate the importance of appropriately de¯ning the loss function used for the estimation of parameters in option pricing models. The implementation of the models is (implicitly or explicitly) always part of a two-step procedure. In a ¯rst step, one estimates the parameters and in a second step, one uses the parameters for model evaluation (pricing out-of-sample). The paper argues that the loss functions used in the in-sample and out-of-sample exercises should be identical to obtain the lowest possible out-of-sample loss. To illustrate the quantitative importance of this methodological issue, we investigate various Mean-Squared-Errors (MSE) for the practitioner Black-Scholes model proposed by Dumas, Fleming and Whaley (1997). We demonstrate that when we use the appropriate loss functions to estimate the out-of-sample MSE of the model can be dramatically reduced. Because this model is used as a benchmark in the option pricing literature, these ¯ndings have important implications for the evaluation of existing and future option pricing models. JEL Classi¯cation: G12 Keywords: option pricing; implied volatility; practitioner Black-Scholes approach; pricing errors; loss functions; out-of sample forecasting; parameter stability. We would like to thank FCAR of Qu¶ebec and SSHRC of Canada for ¯nancial support. Correspondence
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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 | 0.030 | 0.210 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.001 | 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".