Asymptotic properties of duration-based VaR backtests

IF 1.3 Q2 STATISTICS & PROBABILITY

Statistics & Risk Modeling Pub Date : 2022-07-01 DOI:10.1515/strm-2021-0019

Marta Małecka

引用次数: 0

Abstract

Abstract To increase the power of the VaR tests, it has been recently proposed to extend the duration-based test class with the geometric-VaR and Gini-coefficient-based tests. These tests, though exhibiting outstanding power properties, have not gained recognition in the industry. A potential reason is the absence of ready-to-use statistical distributions. To remedy this, we inquire into the limiting properties of these tests and derive relevant asymptotic distributions. We also provide a generalized geometric-VaR test and give its distribution. Through the Monte Carlo study, we show the accuracy of our asymptotic procedures in finite samples, and we find these procedures to be relevant for the current Basel standards. Our theoretical results are illustrated by the empirical study that includes data from the current COVID-19 crisis.

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基于持续时间的VaR回溯检验的渐近性质

摘要为了增加VaR测试的能力，最近有人提出用基于几何VaR和基尼系数的测试来扩展基于持续时间的测试类别。这些测试虽然表现出卓越的功率特性，但尚未在行业中获得认可。一个潜在的原因是缺乏现成的统计分布。为了弥补这一点，我们探讨了这些检验的极限性质，并导出了相关的渐近分布。我们还提供了一个广义几何VaR检验，并给出了它的分布。通过蒙特卡洛研究，我们展示了有限样本中渐近程序的准确性，我们发现这些程序与当前的巴塞尔标准相关。包括当前新冠肺炎危机数据的实证研究说明了我们的理论结果。

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.