HCR & HCR-GARCH – novel statistical learning models for Value at Risk estimation

Michał Woźniak () and Marcin Chlebus ()

No 2021-10, Working Papers from Faculty of Economic Sciences, University of Warsaw

Abstract: Market risk researchers agree that an ideal model for Value at Risk (VaR) estimation does not exist, different models performance strongly depends on current economic circumstances. Under the conditions of sudden volatility increase, such as during the global economic crisis caused by the Covid-19 pandemic, no classical VaR model worked properly even for the group of the largest market indices. Therefore, the aim of the article is to present and formally test three novel statistical learning models for VaR estimation: HCR, HCR-GARCH and HCR-QML-GARCH, which, by considering additional volatility term (due to time context and statistical moments), should be able to perform well in times of market turbulence. In the benchmark procedure we compare the 1% and 2.5% one-day-ahead VaR forecasts obtained with the above models against the estimates of classical methods like: Historical Simulation, KDE, Modified Cornish-Fisher Expansion, GARCH(1,1) with varied distributions, RiskMetrics™, EVT and QML-GARCH. Four periods that vary in terms of market volatility: 2006-9, 2008-11, 2014-17 and mid-2016 to mid-2020 for six different stock market indexes: DAX, WIG 20, MOEX, S&P 500, Nikkei and SHC are selected. Models quality is tested from two perspectives: fulfilling regulatory requirements and forecasting adequateness. Obtained results show that HCR-GARCH outperforms other models during periods of sudden increased volatility in the markets. At the same time, HCR-QML-GARCH liberalizes the conservative estimates of HCR-GARCH and allows its use under moderate volatility, without any major loss of quality in times of crisis.

Keywords: Value at Risk; Hierarchical Correlation Reconstruction; GARCH; Standardized Residuals (search for similar items in EconPapers)
JEL-codes: C52 C53 C58 G32 (search for similar items in EconPapers)
Pages: 37 pages
Date: 2021
New Economics Papers: this item is included in nep-ets, nep-ore and nep-rmg
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Persistent link: https://EconPapers.repec.org/RePEc:war:wpaper:2021-10

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