Comparison of Semi-Parametric and Benchmark Value-At-Risk Models in Several Time Periods with Different Volatility Levels

Abstract

In the literature, there is no consensus as to which Value-at-Risk forecasting model is the best for measuring market risk in banks. In the study an analysis of Value-at-Risk forecasting model quality over varying economic stability periods for main indices from stock exchanges was conducted. The VaR forecasts from GARCH(1,1), GARCH-t(1,1), GARCH-st(1,1), QML-GARCH(1,1), CAViaR and historical simulation models in periods with contrasting volatility trends (increasing, constantly high and decreasing) for countries economically developed (the USA -S&P 500, Germany -DAX and Japan -Nikkei 225) and economically developing (China -SSE COMP, Poland -WIG20 and Turkey -XU100) were compared. The data samples used in the analysis were selected from the period 01.01.1999 -24.03.2017. To assess the VaR forecast quality: excess ratio, Basel traffic light test, coverage tests (Kupiec test, Christoffersen test), Dynamic Quantile test, cost functions and Diebold-Marino test were used. Obtained results show that the quality of Value-at-Risk forecasts for the models varies depending on a volatility trend. However, GARCH-st (1,1) and QML-GARCH(1,1) were found to be the most robust models in the different volatility periods. The results show as well that the CAViaR model forecasts were less appropriate in the increasing volatility period. Moreover, no significant differences for the VaR forecast quality were found for the developed and developing countries. 68"e-Finanse" 2018, vol. 14 / no. 2 Mateusz Buczyński, Marcin Chlebus Comparison of semi-parametric and benchmark value-at-risk models in several time periods with different volatility levels The table above presents the results of formal tests: Kupiec (unconditional coverage), Christoffersen (conditional coverage), and Dynamic Quantile for each analysed index divided by models in all analysed periods. Abbreviations used in the table: UC -p-value of the unconditional coverage test, CC -p-value of the conditional coverage test, DQ -p-value of the Dynamic Quantile test. The number of lags selected in the DQ test is 3. Tests were performed at the 5% significance level. Green fields indicate p-values greater than 5%. Source: Own calculations Mateusz Buczyński, Marcin Chlebus Comparison of semi-parametric and benchmark value-at-risk models in several time periods with different volatility levels www.e-finanse.com University of Information Technology and Management in Rzeszów "e-Finanse" 2018, vol. 14 / no. 2 in growing volatility, the DAX index in constantly high volatility, for the WIG20 index in decreasing volatility, and for S&P500 in none of the analysed periods. 79 www.e-finanse.comUniversity of Information Technology and Management in Rzeszów "e-Finanse" 2018, vol. 14 / no. 2 Mateusz Buczyński, Marcin Chlebus Comparison of semi-parametric and benchmark value-at-risk models in several time periods with different volatility levels 82

Old-fashioned parametric models are still the best: a comparison of value-at-risk approaches in several volatility states

“…Another study conducted by Mutu, Balogh, and Moldovan (2011) proved that EVT and GARCH models perform better than other models in highly volatile periods. Buczyński and Chlebus (2018) also discovered that the GARCH models outperform semiparametric models in turbulent periods, but the discrepancies get smaller in tranquil periods. Additionally, they found that non-parametric methods do perform better in emerging markets.…”

“…Stock markets differ dramatically between states. Many researchers have been comparing the performance of the models before and after turbulent states (among others, in McAleer, Jiménez-Martín, and Pérez-Amaral (2013); Degiannakis, Floros, and Livada (2012); Chlebus (2016); Burchi and Martelli (2016)) and between different stock markets (among others in Žiković (2007); Djaković and Radiscaron (2010); Mutu, Balogh, and Moldovan (2011); Miletic and Miletic (2015); Buczyński and Chlebus (2018)). Most of them notice the advantages of GARCH models in periods of increased volatility, mentioning its conservatism and abrupt fit to the market situation.…”

Combining forecasts? Keep it simple

“…They find that their method is better in assessing the pandemic's effects on energy market interactions. However, to date, no solitary model or method has emerged as the preeminent choice within the realm of VaR forecasting, given the inherent complexities and multifaceted dynamics at play (Bernardi & Catania, 2016;Žiković et al, 2015;Bayer, 2018;Buczyński & Chlebus, 2018).…”