An Empirical Characteristic Function Approach to VaR Under a Mixture-of-Normal Distribution with Time-Varying Volatility
Bibliographic record
Abstract
Calculation of risk measures, such as Value-at-Risk and expected shortfall, requires knowledge of the underlying asset’s or portfolio’s returns distribution. To be realistic, this must be allowed to change over time. GARCH can be a good way to model the random evolution of an asset’s volatility, but standard GARCH assumes the innovation at each time step comes from a normal distribution. The resulting conditionally Gaussian returns therefore have normal, not fat, tails. One way to fatten the tails of the returns distribution is to use a fat-tailed forcing process, such as a Student-t with a low number of degrees of freedom. An alternative approach is to model the returns process as a mixture of normals, but if the distributions that are mixed have constant parameters, the time variation in volatility disappears. In this article, Xu and Wirjanto describe how timevarying fat-tailed densities can be formed by mixing GARCH processes together. Performance comparisons against other models in calculating the tail risks for exchange rates on four currencies show that the GARCH mixture model works very well. TOPICS:Derivatives, tail risks, VAR and use of alternative risk measures of trading risk
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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 | 0.004 | 0.015 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.003 |
| 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".