Working Papers

The WNE Working Papers series has been published by the Faculty of Economic Sciences at the University of Warsaw since 2008.

The WNE Working Papers series provides a fast, open channel for disseminating research conducted at the Faculty of Economic Sciences, University of Warsaw. The papers hosted here are working versions (pre-prints) and may evolve as authors refine their analyses, incorporate feedback, or progress through formal peer-review. What you read is the current version released by the authors, timestamped and assigned DOI/ISSN identifiers to ensure precise citation and version tracking. Copyright remains with the authors, who may, at any time, upload a revised file or add a note directing readers to a later, peer-reviewed publication.

The Working Papers series accepts articles by research employees of the Faculty and publications from conferences organised at the Faculty of Economic Sciences at the University of Warsaw. Articles should be original research papers which have not been previously published, on the subject of economics.

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Number of Results 7

WP(28/2021)376. The effectiveness of Value-at-Risk models in various volatility regimes

Authors: Schiffers Aleksander, Chlebus Marcin
There is an ongoing discussion, what is the most efficient approach to Value-at-Risk estimation. Subsequent studies and meta-analyzes show that there is no scientific consensus in this field and the necessity of further research is frequently underli…

WP376. The effectiveness of Value-at-Risk models in various volatility regimes

There is an ongoing discussion, what is the most efficient approach to Value-at-Risk estimation. Subsequent studies and meta-analyzes show that there is no scientific consensus in this field and the necessity of further research is frequently underlined. In this study, authors try to assess the comparative performance of models used for Value-at-Risk estimations in changing market volatility regimes. The models considered are: the Historical Simulation, the Risk Metrics®, the GARCH(1,1)-n, the GARCH(1,1)-t, the GARCH(1,1)-st, the GARCH(1,1)-QML. GARCH models are additionally enriched with additional, exogenous regressors in the form of lagged commodity futures contracts returns. The analysis is conducted on a set of utility sector stock indices from six developed countries across the globe: WIG Energia (Poland), Dow Jones Utilities Average (USA), CAC Utilities (France), Tokyo SE Topix-17 Power & Gas (Japan), S&P ASX 200 Utilities (Australia), and DAX All Utilities (Germany). Three samples of different characteristics are distinguished from the last 10 years of data and one of them covers the upsurge in market volatility caused by the Covid-19 pandemic. In order to evaluate the VaR forecasts performance of each model, conditional/unconditional coverage tests of Kupiec and Christoffersen, Dynamic Quantile test, and Diebold-Marino test were used. Empirical results of the study indicate that in the volatile market periods, overall quality of forecasts deteriorates for all models to a varying degree. However, the GARCH(1,1)-st with external regressors is considered the most efficient and robust model due to its ability to capture stylized facts of data distribution. Exogenous variables are worth considering but their contribution to performance improvement may be model and market dependent.


Schiffers Aleksander, Chlebus Marcin
risk management market risk Value-at-risk GARCH Historical Simulation Risk Metrics® risk modelling benchmark model quality assessment

WP(11/2021)359. Comparison of the accuracy in VaR forecasting for commodities using different methods of combining forecasts

Authors: Lis Szymon, Chlebus Marcin
No model dominates existing VaR forecasting comparisons. This problem may be solved by combine forecasts. This study investigates the daily volatility forecasting for commodities (gold, silver, oil, gas, copper) from 2000-2020 and identifies the sour…

WP359. Comparison of the accuracy in VaR forecasting for commodities using different methods of combining forecasts

No model dominates existing VaR forecasting comparisons. This problem may be solved by combine forecasts. This study investigates the daily volatility forecasting for commodities (gold, silver, oil, gas, copper) from 2000-2020 and identifies the source of performance improvements between individual GARCH models and combining forecasts methods (mean, the lowest, the highest, CQOM, quantile regression with the elastic net or LASSO regularization, random forests, gradient boosting, neural network) through the MCS. Results indicate that individual models achieve more accurate VaR forecasts for the confidence level of 0.975, but combined forecasts are more precise for 0.99. In most cases simple combining methods (mean or the lowest VaR) are the best. Such evidence demonstrates that combining forecasts is important to get better results from the existing models. The study shows that combining the forecasts allows for more accurate VaR forecasting, although it's difficult to find accurate, complex methods.


Lis Szymon, Chlebus Marcin
Combining forecasts Econometric models Finance Financial markets GARCH models Neural networks Regression Time series Risk Value-at-Risk Machine learning Model Confidence Set

WP(8/2021)356. GARCHNet - Value-at-Risk forecasting with novel approach to GARCH models based on neural networks

Authors: Buczyński Mateusz, Chlebus Marcin
This study proposes a new GARCH specification, adapting a long short-term memory (LSTM) neural network's architecture. Classical GARCH models have been proven to give substantially good results in the case of financial modeling, where high volati…

WP356. GARCHNet - Value-at-Risk forecasting with novel approach to GARCH models based on neural networks

This study proposes a new GARCH specification, adapting a long short-term memory (LSTM) neural network's architecture. Classical GARCH models have been proven to give substantially good results in the case of financial modeling, where high volatility can be observed. In particular, their high value is often praised in the case of Value-at-Risk. However, the lack of nonlinear structure in most of the approaches entails that the conditional variance is not represented in the model well enough. On the contrary, recent rapid advancement of deep learning methods is said to be capable of describing any nonlinear relationships prominently. We suggest GARCHNet - a nonlinear approach to conditional variance that combines LSTM neural networks with maximum likelihood estimators of probability in GARCH. The distributions of the innovations considered in the paper are: normal, t and skewed t, however the approach does enable extensions to other distributions as well. To evaluate our model, we have executed an empirical study on the log returns of WIG 20 (Warsaw Stock Exchange Index) in four different time periods throughout 2005 and 2021 with varying levels of observed volatility. Our findings confirm the validity of the solution, however we present several directions to develop it further.


Buczyński Mateusz, Chlebus Marcin
Value-at-Risk GARCH neural networks LSTM

WP(28/2020)334. Value-at-risk — the comparison of state-of-the-art models on various assets

Authors: Kielak Karol, Ślepaczuk Robert
This paper compares different approaches to Value-at-Risk measurement based on parametric and non-parametric approaches. Three portfolios are taken into consideration — the first one containing only stocks from the London Stock Exchange, the se…

WP334. Value-at-risk — the comparison of state-of-the-art models on various assets

This paper compares different approaches to Value-at-Risk measurement based on parametric and non-parametric approaches. Three portfolios are taken into consideration — the first one containing only stocks from the London Stock Exchange, the second one based on different assets of various origins and the third one consisting of cryptocurrencies. Data used cover the period of more than 20y. In the empirical part of the study, parametric methods based on mean-variance framework are compared with GARCH(1,1) and EGARCH(1,1) models. Different assumptions concerning returns' distribution are taken into consideration. Adjustment for the fat tails effect is made by using Student t distribution in the analysis. One-day-ahead 95%VaR estimation is then calculated. Thereafter, models are validated using Kupiec and Christoffersen tests and Monte Carlo Simulation for reliable verification of the hypotheses. The overall goal of this paper is to establish if analyzed models accurately estimate Value-at-Risk measure, especially if we take into account assets with various returns distribution characteristics.


Kielak Karol, Ślepaczuk Robert
risk management Value-at-Risk GARCH models returns distribution Monte Carlo Simulation asset class cryptocurrencies

WP(12/2019)297. Old-fashioned parametric models are still the best. A comparison of Value-at-Risk approaches in several volatility states

Authors: Buczyński Mateusz, Chlebus Marcin
Numerous advances in the modelling techniques of Value-at-Risk (VaR) have provided the financial institutions with a wide scope of market risk approaches. Yet it remains unknown which of the models should be used depending on the state of volatility.…

WP297. Old-fashioned parametric models are still the best. A comparison of Value-at-Risk approaches in several volatility states

Numerous advances in the modelling techniques of Value-at-Risk (VaR) have provided the financial institutions with a wide scope of market risk approaches. Yet it remains unknown which of the models should be used depending on the state of volatility. In this article we present the backtesting results for 1% and 2.5% VaR of six indexes from emerging and developed countries using several most known VaR models, among many: GARCH, EVT, CAViaR and FHS with multiple sets of parameters. The backtesting procedure has been based on the excess ratio, Kupiec and Christoffersen tests for multiple thresholds and cost functions. The added value of this article is that we have compared the models in four different scenarios, with different states of volatility in training and testing samples. The results indicate that the best of the models that is the least affected by changes in the volatility is GARCH(1,1) with standardized student's t-distribution. Non-parmetric techniques (e.g. CAViaR with GARCH setup (see Engle and Manganelli, 2001) or FHS with skewed normal distribution) have very prominent results in testing periods with low volatility, but are relatively worse in the turbulent periods. We have also discussed an automatic method to setting a threshold of extreme distribution for EVT models, as well as several ensembling methods for VaR, among which minimum of best models has been proven to have very good results - in particular a minimum of GARCH(1,1) with standardized student's t-distribution and either EVT or CAViaR models.


Buczyński Mateusz, Chlebus Marcin
Value-at-Risk GARCH Extreme Value Theory Filtered Historical Simulation CAViaR market risk forecast comparison

WP(6/2016)197. EWS-GARCH: New Regime Switching Approach to Forecast Value-at-Risk

Authors: Chlebus Marcin
In the study a proposal of two-step EWS-GARCH models to forecast Value-at-Risk is presented. The EWS-GARCH allows different distributions of returns to be used in Value-at-Risk forecasting depending on a forecasted state of the financial time series.…

WP197. EWS-GARCH: New Regime Switching Approach to Forecast Value-at-Risk

In the study a proposal of two-step EWS-GARCH models to forecast Value-at-Risk is presented. The EWS-GARCH allows different distributions of returns to be used in Value-at-Risk forecasting depending on a forecasted state of the financial time series. In the study EWS-GARCH with GARCH(1,1) and GARCH(1,1) with the amendment to the empirical distribution of returns as a Value-at-Risk model in a state of tranquillity and empirical tail, exponential or Pareto distributions used to forecast Value-at-Risk in a state of turbulence were considered. The evaluation of the quality of the Value-at-Risk forecasts was based on the Value-at-Risk forecasts adequacy (the excess ratio, the Kupiec test, the Christoffersen test, the asymptotic test of unconditional coverage and the back-testing criteria defined by the Basel committee) and the analysis of loss functions (the Lopez quadratic loss function, the Abad & Benito absolute loss function, the 3rd version of Caporin loss function and proposed in the study the function of excessive costs). Obtained results indicate that the EWS-GARCH models may improve the quality of the Value-at-Risk forecasts generated using benchmark models. However, the choice of best assumptions for an EWS-GARCH model should depend on the goals of the Value-at-Risk forecasting model. The final selection may depend on an expected level of adequacy, conservatism and costs of a model.


Chlebus Marcin
Value-at-Risk GARCH forecasting state of turbulence regime switching risk management risk measure market risk.

WP(3/2015)151. Bivariate GARCH models for single asset returns

Authors: Skoczylas Tomasz
In this paper an alternative approach to modelling and forecasting single asset returns volatility is presented. A new, bivariate, flexible framework, which may be considered as a development of single-equation ARCH-type models, is proposed. This app…

WP151. Bivariate GARCH models for single asset returns

In this paper an alternative approach to modelling and forecasting single asset returns volatility is presented. A new, bivariate, flexible framework, which may be considered as a development of single-equation ARCH-type models, is proposed. This approach focuses on joint distribution of returns and observed volatility, measured by Garman-Klass variance estimator, and it enables to examine simultaneous dependencies between them. Proposed models are compared with benchmark GARCH and range-based GARCH (RGARCH) models in terms of prediction accuracy. All models are estimated with maximum likelihood method, using time series of EUR/PLN spot rate quotations and WIG20 index. Results are very encouraging especially for foreasting Value-at-Risk. Bivariate models achieved lesser rates of VaR exception, as well as lower coverage tests statistics, without being more conservative than its single-equation counterparts, as their forecasts errors measures are rather similar.


Skoczylas Tomasz
bivariate volatility models joint distribution range-based volatility estimators Garman-Klass estimator observed volatility volatility modelling GARCH leverage Value-at-Risk volatility forecasting
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