Principal component models with stochastic mean‐reverting levels. Pricing and covariance surface improvements
Bibliographic record
Abstract
In this work, we create a family of simple stochastic covariance models, which display stochastic mean‐reverting levels of covariance as an additional level of stochastic behavior beyond well‐known stochastic volatility and correlation. The one‐dimensional version of our model is inspired by Heston model, while the multidimensional model generalizes the principal component stochastic volatility model. Their main contribution is that they capture stochastic mean‐reversion levels on the volatility and on the eigenvalues of the instantaneous covariance matrix of the vector of stock prices, with direct implications on the correlations as well. Our focus is on the multidimensional model; we investigate its properties and derive a closed‐form expression for the characteristic function. This allows us to study the pricing of financial derivatives, such as correlation and spread options. Those prices are compared with simulated Monte Carlo prices for correctness. A sensitivity analysis is performed on the parameters of the stochastic mean‐reverting level of volatilities to study their impact on the price. Finally, implied volatility curves and correlation surfaces are built to reveal the additional flexibility gained within the new model. Copyright © 2016 John Wiley & Sons, Ltd.
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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 | 0.002 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 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".