Best Fitting Fat Tail Distribution for the Volatilities of Energy Futures: Gev, Gat and Stable Distributions in GARCH and APARCH Models
Bibliographic record
Abstract
Precise modeling and forecasting of the volatility of energy futures is vital to structuring trading strategies in spot markets for risk managers. Capturing conditional distribution, fat tails and price spikes properly is crucial to the correct measurement of risk. This paper is an attempt to model volatility of energy futures under different distributions. In empirical analysis, we estimate the volatility of Natural Gas Futures, Brent Oil Futures and Heating Oil Futures through GARCH and APARCH models under gev, gat and alpha-stable distributions. We also applied various VaR analyses, Gaussian, Historical and Modified (Cornish-Fisher) VaR, for each variable. Results suggest that the APARCH model largely outperforms the GARCH model, and gat distribution performs better in modeling fat tails in returns. Our results also indicate that the correct volatility level, in gat distribution, is higher than those suggested under normal distribution with rates of 56%, 45% and 67% for Natural Gas Futures, Brent Oil Futures and Heating Oil Futures, respectively. Implemented VaR analyses also support this conclusion. Additionally, VaR test results demonstrate that energy futures display riskier behavior than S&P 500 returns. Our findings suggest that for optimum risk management and trading strategies, risk managers should consider alternative distributions in their models. According to our results, prices in energy markets are wilder than the perception of normal distribution. In this regard, regulators and policy makers should enhance transparency and competitiveness in the energy markets to protect consumers.
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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 | 0.003 | 0.012 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".