Old-fashioned parametric models are still the best. A comparison of Value-at-Risk approaches in several volatility states. M Ma at te eu us sz z B Bu uc cz zy yń ńs sk ki i* *, , M Ma ar rc ci in n C Ch hl le eb bu us s
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
This paper proposes a new GARCH specification that adapts the architecture of a long-term short memory neural network (LSTM). It is shown that classical GARCH models generally give good results in financial modeling, where high volatility can be observed. In particular, their high value is often praised in Value-at-Risk. However, the lack of nonlinear structure in most approaches means that conditional variance is not adequately represented in the model. On the contrary, the recent rapid development of deep learning methods is able to describe any nonlinear relationship in a clear way. We propose GARCHNet, a nonlinear approach to conditional variance that combines LSTM neural networks with maximum likelihood estimators in GARCH. The variance distributions considered in the paper are normal, t and skewed t, but the approach allows extension to other distributions. To evaluate our model, we conducted an empirical study on the logarithmic returns of the WIG 20 (Warsaw Stock Exchange Index), S&P 500 (Standard & Poor’s 500) and FTSE 100 (Financial Times Stock Exchange) indices over four different time periods from 2005 to 2021 with different levels of observed volatility. Our results confirm the validity of the solution, but we provide some directions for its further development.
This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).
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