Time-consistency of risk measures with GARCH volatilities and their estimation

IF 1.3 Q2 STATISTICS & PROBABILITY

Statistics & Risk Modeling Pub Date : 2015-04-18 DOI:10.1515/strm-2015-0010

C. Klüppelberg, Jianing Zhang

引用次数: 3

Abstract

Abstract 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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GARCH波动率风险度量的时间一致性及其估计

摘要本文研究由GARCH(1,1)模型给出的收益的时间一致风险度量。我们提出了一种基于静态风险度量的构建方法，克服了缺乏时间一致性的问题。然后，我们详细研究了风险度量的VaR和AVaR的构造。虽然在VaR情况下，我们可以推导出其时间一致对应的解析公式，但在AVaR情况下，我们推导出其时间一致版本的下界和上界。此外，我们结合了极值理论(EVT)的技术，以允许对相应的风险度量进行更多的尾部统计分析。最后，我们将我们的结果应用于股票价格数据集。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Statistics & Risk Modeling STATISTICS & PROBABILITY-

CiteScore

1.80

自引率

6.70%

发文量

期刊介绍： Statistics & Risk Modeling (STRM) aims at covering modern methods of statistics and probabilistic modeling, and their applications to risk management in finance, insurance and related areas. The journal also welcomes articles related to nonparametric statistical methods and stochastic processes. Papers on innovative applications of statistical modeling and inference in risk management are also encouraged. Topics Statistical analysis for models in finance and insurance Credit-, market- and operational risk models Models for systemic risk Risk management Nonparametric statistical inference Statistical analysis of stochastic processes Stochastics in finance and insurance Decision making under uncertainty.