Kolmogorov-Smirnov test.

Jet fuel plays a crucial role as an essential energy source in aerospace and aviation operations. The recent increase in fuel prices has presented airlines with the new challenge of managing jet fuel costs to ensure consistent cash flow and minimize operational uncertainties. The conventional risk prediction models used by airlines often assume that risks are normally distributed according to the classical Central Limit Theorem, which can lead to under-hedging. This paper proposes an innovative approach using the stable Paretian model to analyze the price return of jet fuel in large samples. It comprehensively compares the fitting effect of the stable Paretian distribution with that of the normal distribution based on specific criteria and non-parametric significance tests. Furthermore, it investigates the accuracy of risk measures such as Value at Risk (VaR) and Conditional Value at Risk (CVaR) predicted by both models. In addition to comparing differences in VaR between predicted values and actual values, this paper provides a more comprehensive comparison of risk measures under rolling window forecast situation. Results suggest that despite indistinguishable results in VaR backtest, the stable Paretian distribution has a overall better fitting effect as well as a less biased predicted CVaR based on the AIC of -14099.46, BIC of -14110.98, p = 0.58 in Kolmogorov-Smirnov test and p = 0.46(0.92) in the 0.01(0.05) significance level of Expected Shortfall Regression Test. This might be explained by its ability to capture asset return dynamics while maintaining shape stability with few parameters. This research can provide valuable insights for guiding airlines’ risk management decisions. its ability to capture asset return dynamics while maintaining shape stability with few parameters. This research can provide valuable insights for guiding airlines’ risk management decisions.航空煤油作为航空航天与民航运营不可或缺的核心能源，发挥着至关重要的作用。近期燃油价格上涨给航空公司带来了新的挑战：需合理管控航空煤油成本，以保障现金流稳定并最大程度降低运营不确定性。当前航空公司所采用的传统风险预测模型，通常基于经典中心极限定理假设风险服从正态分布，这一假设可能引发对冲不足的问题。本文提出一种创新性研究方法，采用稳定帕累托模型（stable Paretian model）对大样本下的航空煤油价格收益率展开分析。基于特定评判标准与非参数显著性检验，本文全面对比了稳定帕累托分布与正态分布的拟合效果。此外，本文还探究了两种模型所预测的两类风险测度指标的准确性，即风险价值（Value at Risk, VaR）与条件风险价值（Conditional Value at Risk, CVaR）。除对比预测VaR与实际值的差异外，本文还在滚动窗口预测场景下，对风险测度展开了更为全面的对比分析。研究结果表明，尽管在VaR回测中二者表现无显著差异，但基于赤池信息准则（AIC）值为-14099.46、贝叶斯信息准则（BIC）值为-14110.98，科尔莫戈罗夫-斯米尔诺夫（Kolmogorov-Smirnov）检验p值为0.58，以及期望短缺回归检验在0.01（0.05）显著性水平下的p值为0.46（0.92），稳定帕累托分布整体具备更优的拟合效果，且其预测得到的CVaR偏差更低。这一现象可归因于其能够捕捉资产收益率的动态特征，同时仅需少量参数即可维持分布形状的稳定性。本研究可为航空公司的风险管理决策提供极具价值的参考依据。