Asymmetric power distribution: Theory and applications to risk measurement
非对称幂分布：理论及风险度量应用AI 解读 ↓
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非对称幂分布：理论及风险度量应用
- 研究问题
- 研究如何用灵活的非对称分布估计金融收益的预期短缺，以及不同条件异方差模型的尾部风险预测表现。
- 方法与思路
- 作者构建非对称幂分布，推导分位数、预期短缺及极大似然估计的渐近性质，并开展模拟和样本外比较。
- 材料陈述的贡献
- 摘要称给出解析得分与一致协方差估计；预测比较中 GPD–EGARCH 在百分之一尾部似较好，其余两档表现相当。
- 阅读关注点
- 应核对分布参数限制、渐近推导条件，以及预期短缺预测的评价准则、样本外设计和模型间比较依据。
- 阅读边界
- 仅据所给 Crossref 摘要，不能认定非对称幂分布普遍优于其他模型；四个市场序列的具体构成和预测差异未说明。
原文摘要
Abstract Theoretical literature in finance has shown that the risk of financial time series can be well quantified by their expected shortfall, also known as the tail value‐at‐risk. In this paper, I construct a parametric estimator for the expected shortfall based on a flexible family of densities, called the asymmetric power distribution (APD). The APD family extends the generalized power distribution to cases where the data exhibits asymmetry. The first contribution of the paper is to provide a detailed description of the properties of an APD random variable, such as its quantiles and expected shortfall. The second contribution of the paper is to derive the asymptotic distribution of the APD maximum likelihood estimator (MLE) and construct a consistent estimator for its asymptotic covariance matrix. The latter is based on the APD score whose analytic expression is also provided. A small Monte Carlo experiment examines the small sample properties of the MLE and the empirical coverage of its confidence intervals. An empirical application to four daily financial market series reveals that returns tend to be asymmetric, with innovations which cannot be modeled by either Laplace (double‐exponential) or Gaussian distribution, even if we allow the latter to be asymmetric. In an out‐of‐sample exercise, I compare the performances of the expected shortfall forecasts based on the APD‐GARCH, Skew‐ t ‐GARCH and GPD‐EGARCH models. While the GPD‐EGARCH 1% expected shortfall forecasts seem to outperform the competitors, all three models perform equally well at forecasting the 5% and 10% expected shortfall. Copyright © 2007 John Wiley & Sons, Ltd.