Which pricing approach for options under GARCH with non-normal innovations?
Bibliographic record
Abstract
Two different pricing frameworks are typically used in the literature when pricing options under GARCH with non-normal innovations: the equilibrium approach and the no-arbitrage approach.Each framework can accommodate various forms of GARCH and innovation distributions, but empirical implementation and tests are typically done in one framework or the other because of the computational challenges that are involved in obtaining the relevant pricing parameters.We contribute to the literature by comparing and documenting the empirical performance of a GARCH specification which can be readily implemented in both pricing frameworks.The model uses a parsimonious GARCH specification with skewed and leptokurtic Johnson s u innovations together with either the equilibrium based framework or the no-arbitrage based framework.Using a large sample of options on the S&P 500 index, we find that the two approaches give rise to very similar pricing errors when implemented with time-varying pricing parameters.However, when implemented with constant pricing parameters, the performance of the no-arbitrage approach deteriorates in periods of high volatility relative to the equilibrium approach whose performance remains stable and at par with the models with time-varying pricing parameters.
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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 | 0.007 | 0.031 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.008 |
| Open science | 0.003 | 0.001 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.005 | 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".