Discussion and Empirical Analysis of Coherent Risk Measure
Date Issued
2006
Date
2006
Author(s)
Lin, Keng-Peng
DOI
zh-TW
Abstract
There are many reasons to develop risk measurement system. Two general uses of such a system are to quantify and to compare risk. Keeping this in mind, we must ensure any risk measurement system produces coherent result. The coherency of a risk measure has been discussed in Artzner et al. (1997、1999). He also proposed Conditional Tail Expectation as a coherent risk measure. Furthermore, coherent risk measure derived from distortion functions has later been discussed in Wang〈1996〉.
In the first section of this study, we consider some distortion functions and discuss relationship between each risk measure and the parameter. We have also compared different distortion functions. We present that we can obtain larger risk measure of the loss data which is right skewed by using Proportional Hazards Distortion rather than using Dual Power Distortion.
In this paper we also conduct empirical study on the returns of eight industry indexes both in the long run and in the short run. We state the characteristics of each risk measure by using historical simulation approach. And we obtain that :
1. As to the long-term research, when VaR is adopted as a risk measure, the VaR which is calculated from the loss data censored at zero is suggested to be referable. If we want to reflect the skew of the loss distribution, Proportional Hazards distortion would be a good choice.
2. In the short-run analysis, there’s no significant difference between different risk measures. The coherent risk measure CTE is easily understood. In order to save our time, it may be the best choice.
Subjects
風險衡量
變形函數
風險值
條件尾端期望值
Coherent Risk Measure
Distortion Function
VaR
Conditional Tail Expection
Type
thesis
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