具有GARCH波动率的风险测度的时间相合性及其估计
Time-consistency of risk measures with GARCH volatilities and their estimation
摘要：
在本文中，我们研究的时间一致的风险措施的回报率，由一个GARCH（1，1）模型。我们提出了一个建设的风险措施的基础上，克服了缺乏时间一致性的静态同行。然后，我们详细研究了我们的风险度量值的风险价值（VaR）和平均风险价值（AVaR）的建设。而在风险值的情况下，我们可以推导出一个分析公式，其时间一致的对应，在AVaR的情况下，我们推导出其时间一致的版本的下限和上限。此外，我们将技术从极值理论（EVT），以允许更多的尾部调整相应的风险措施的统计分析。最后，我们将我们的结果应用到一组股票价格的数据中。
英文摘要：
In this paper we study time-consistent risk measures for returns that are given by a GARCH(1,1) model. We present a construction of risk measures based on their static counterparts that overcomes the lack of time-consistency. We then study in detail our construction for the risk measures Value-at-Risk (VaR) and Average Value-at-Risk (AVaR). While in the VaR case we can derive an analytical formula for its time-consistent counterpart, in the AVaR case we derive lower and upper bounds to its time-consistent version. Furthermore, we incorporate techniques from Extreme Value Theory (EVT) to allow for a more tail-geared statistical analysis of the corresponding risk measures. We conclude with an application of our results to a data set of stock prices.
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