The Cornish-Fisher-Expansion in the Context of Delta - Gamma - Normal Approximations
The Cornish-Fisher-Expansion in the Context of Delta - Gamma - Normal Approximations
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DOI：
10.21314/jor.2002.068
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发表时间：
2002-07
期刊：
影响因子：
0.7
通讯作者：
S. Jaschke
中科院分区：
文献类型：
--
作者：
S. Jaschke
提出了在计算风险价值的 Delta-Gamma-Normal 方法的背景下 Cornish-Fisher-Expansion 的定性和定量特性。康沃尔-费舍尔展开式的一些定性缺陷——分布函数的单调性以及收敛性得不到保证——使它看起来没有吸引力。然而，在许多实际情况下，其实际精度绰绰有余，并且与数值傅里叶反演等其他方法相比，Cornish-Fisher 近似的计算速度更快（且更简单）。本文试图就在这种情况下何时和何时不使用 Cornish-Fisher 提供一个平衡的观点。
Qualitative and quantitative properties of the Cornish-Fisher-Expansion in the context of Delta-Gamma-Normal approaches to the computation of Value at Risk are presented. Some qualitative deficiencies of the Cornish-Fisher-Expansion – the monotonicity of the distribution function as well as convergence are not guaranteed – make it seem unattractive. In many practical situations, however, its actual accuracy is more than sufficient and the Cornish-Fisher-approximation can be computed faster (and simpler) than other methods like numerical Fourier inversion. This paper tries to provide a balanced view on when and when not to use Cornish-Fisher in this context.