Approximating the distributions of estimators of financial risk under an asymmetric Laplace law
Approximating the distributions of estimators of financial risk under an asymmetric Laplace law
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DOI：
10.1016/j.csda.2006.08.004
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发表时间：
2007-04
期刊：
影响因子：
--
通讯作者：
A. Trindade;Yun Zhu
中科院分区：
文献类型：
--
作者：
A. Trindade;Yun Zhu
在非对称拉普拉斯（AL）分布随机抽样下，给出了金融风险的两种度量--风险价值（VaR）和条件风险价值（CVaR）的参数和非参数估计（NPE）的显式表达式.渐近分布是在非常一般的条件下建立的。有限样本分布的鞍点逼近的手段进行了研究。后者是高度计算密集型的，需要新的方法来近似的时刻和特殊的功能，出现在评价的时刻生成函数。由此产生的密度函数图揭示了新的估计质量。计算CVaR表明，NPE享有更大的渐近效率相对于参数估计比的情况下，风险值。货币汇率建模的方法的应用表明，AL分布是成功地捕捉peakedness，leptokurticity，偏态，固有的这些数据。在由此产生的参数为基础的推理表现出的优越性提供了一个重要的信息，医生。
Explicit expressions are derived for parametric and nonparametric estimators (NPEs) of two measures of financial risk, value-at-risk (VaR) and conditional value-at-risk (CVaR), under random sampling from the asymmetric Laplace (AL) distribution. Asymptotic distributions are established under very general conditions. Finite sample distributions are investigated by means of saddlepoint approximations. The latter are highly computationally intensive, requiring novel approaches to approximate moments and special functions that arise in the evaluation of the moment generating functions. Plots of the resulting density functions shed new light on the quality of the estimators. Calculations for CVaR reveal that the NPE enjoys greater asymptotic efficiency relative to the parametric estimator than is the case for VaR. An application of the methodology in modeling currency exchange rates suggests that the AL distribution is successful in capturing the peakedness, leptokurticity, and skewness, inherent in such data. A demonstrated superiority in the resulting parametric-based inferences delivers an important message to the practitioner.