Search results

1

Porównanie metod estymacji VaR na polskim rynku gazu

100%

Ganczarek-Gamrot A.

Studia Ekonomiczne

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2015

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vol. 219

41-52

PL

Celem pracy jest przeprowadzenie analizy porównawczej metod estymacji ryzyka zmiany ceny gazu oszacowanego za pomocą Value-at-Risk (VaR). W pracy do porównania efektywności estymacji ryzyka zmiany ceny gazu wybrano metodę symula-cji Monte Carlo, w której VaR traktowany jest jako kwantyl rozkładu zmiennej losowej o rozkładzie normalnym, t-Studenta, GED oraz skośnym rozkładzie t-Studenta z VaR oszacowanym z uwzględnieniem dynamiki zmienności cen gazu za pomocą liniowych oraz nieliniowych modeli szeregów czasowych AR-GARCH. Analiza porównawcza została przeprowadzona w oparciu o wyniki testu przekroczeń Kupca na podstawie logarytmicznych stóp zwrotu wartości indeksu gas_ base notowanego na Rynku Dnia Następnego (RDN) TGE w okresie od 1 stycznia do 20 listopada 2014 roku.

EN

This work is aimed at comparing methods of Value-at-Risk (VaR) estimation on Polish natural gas market. Two methods of calculating VaR were examined. One of them uses a quantile of the normal, t-Student, skewed t-Student or GED distribution. Another method is based on AR-GARCH models. Empirical analysis was carried out for logarithmic rates of return of gas-base index noted on the Day Ahead Market from 1th January to 20th November 2014. Based on Kupiec test results one may say that on Polish natural gas market VaR estimates calculated by time series models are more appropriate than VaR estimates calculated as a quantile of distribution.

2

Weryfikacja historyczna modeli wartości zagrożonej – zastosowanie wybranych metod dla rynku polskiego w okresie kryzysu finansowego

94%

Lusztyn M.

Econometrics. Ekonometria. Advances in Applied Data Analytics

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2013

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issue 4(42)

117-129

EN

Several banks use internal Value at Risk models to measure market risk and to calculate regulatory capital necessary to cover that risk. Backtesting is a statistical tool that allows differentiating precise and imprecise risk models. The objective of this paper is to backtest selected Value at Risk models in a period preceding and during the financial crisis, based on the example of Polish currency, equity and bond markets. The obtained results do not justify unequivocal statistical acceptance of any of the analyzed models. This in turn suggest extreme caution in using Value at Risk as the only quantitative risk management tool. Stable and cautious risk management of a financial institution calls for supplementing Value at Risk with alternative risk measures.

3

THE USE OF A VALUE AT RISK MEASURE FOR THE ANALYSIS OF BANK INTEREST MARGINS

94%

Gemzik-Salwach, A.

Finansowy Kwartalnik Internetowy e-Finanse

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2012

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vol. 8

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issue 4

15-29

EN

The article describes the use of a Value at Risk measure to analyze the effectiveness of a bank. Among various existing possibilities of using this measure, the use of a new method has been proposed, namely, correcting various indicators of bank interest margins by using the Value at Risk measure. The newly established measures were then subjected to empirical tests, whose main objective was to test the capacity of the information resulting from the recourse to the proposed indicators. Using the data from financial statements of banks listed on the Stock Exchange in Warsaw in the years 1998-2012, two types of risk-adjusted bank interest margins were calculated, which provided a way to set the minimum levels that can be expected with the probability assumed in the calculation. The way in which these values are formed over time was then analyzed and they were finally compared with the typical values.

4

Zastosowanie funkcji łączących w wyznaczaniu granic dla Value-at-Risk

94%

Szkutnik T.

Zeszyty Naukowe Uniwersytetu Ekonomicznego w Krakowie

|

2012

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issue 895

59-70

EN

The subject of the article concerns bank risk generally and addresses the problem of determining relevant limits for the VaR risk measure at the aggregated level for dependent random variables whose joint multidimensional distribution function is unknown. The information about the dependencies between the random variables is regarded as partial, which allows for the introduction of limiting conditions for the unknown distribution function and the determination of limits for VaR. The dependences among the random variables were introduced on the ground of copula function theory. Limits for the aggregated VaR value were determined on the basis of Williamson and Downson numerical algorithm by means of the programme MATLAB.

5

ARIMA-GARCH MODELS IN ESTIMATING MARKET RISK USING VALUE AT RISK FOR THE WIG20 INDEX

94%

Makiel K.

Finansowy Kwartalnik Internetowy e-Finanse

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2012

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vol. 8

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issue 2

25-33

EN

This paper determines whether the VaR estimation is influenced by conditional distribution of return rates (normal, t-student, GED) and attempts to choose the model which best estimates VaR on a selected example. We considered logarithmic return rates for the WIG-20 index from 1999-2011. Then, on their basis we estimates various types of ARIMA-GARCH (1,1) models. Applying relevant models we calculated VaR for the long and short position. The differences between the models were settled on the basis of the Kupiec test.

6

Modele zmienności w kalkulacjach Value at Risk ocena i dobór modelu

94%

Letkowski D.

Zarządzanie i Finanse

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2013

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vol. 1

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issue 3

245-260

PL

Wykorzystanie modeli wartości zagrożonej (VaR) w praktyce zarządzania finansowego stale rośnie, ze względu na użyteczność odnośnie pomiaru ryzyka finansowego oraz wykorzystania VaR do ustanawiania limitów kapitałowych, płynności, czy zabezpieczeń. Obecne warunki rynkowe cechuje znaczna zmienność parametrów, które determinują wartości wyliczanych modelami VaR wyników. Z definicji VaR wynika, że kluczowe znaczenie dla poprawności wyników modeli VaR ma dobór modeli zmienności. Artykuł opisuje i ocenia cztery modele zmienności: odchylenie standardowe, prostą kwadratową średnią ruchomą, model zmienności GARCH oraz model EWMA. Szczególna uwaga została poświęcona konstrukcji miar zmienności oraz zachowaniu modeli zmienności, tzn. odwzorowywaniu zmian empirycznych przez modele zmienności. Analizy obrazują, że znaczenie ma nie tylko dobór modelu zmienności ale również jego kalibracja, tzn. odpowiednie dobranie okresu, z którego wyprowadzana jest zmienność. W konkluzji stwierdzono, że modele VaR zapewniają dostateczny poziom precyzji szacunków ryzyka, pod warunkiem, że wykorzystywane są właściwie skalibrowane modele zmienności w określonym kontekście zarządzania.

7

The application of generalized pareto distribution and copula functions in the issue of operational risk

94%

Basiaga K., Szkutnik T.

Econometrics. Ekonometria. Advances in Applied Data Analytics

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2013

|

issue 1(39)

133-143

EN

The article concerns the issue of modelling of operational risk in a bank. The area of analysis is related to two separate analytical areas composed of certain combinations of the Basel Matrix risk categories. The focus of interest is in the modelling of loss severity distributions in LDA models and in consideration of the power and character of dependences among the studied analytical areas. To model a single loss severity distribution, the authors used the approach based on extreme values theory EVT. GPD distribution was used to model the right tail. The t-Student copula function was used in the cases of consideration of power and character of dependences. The determined values describe the effects of the applied approach in relative scale.

8

Comparison of Alternative Approaches to VaR Evaluation

94%

Łupiński M.

Ekonomia. Rynek, Gospodarka, Społeczeństwo

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2013

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issue 33

127-143

EN

The main goal of this article is to present alternative methods of market risk measurement in Polish banking sector with popular Value at Risk (VaR) approach. Four main methods: analytical, historical, simulation and hybrid (Filtered Historical Simulation, FHS) of VaR are presented and then three of them are applied to evaluate interest risk stemming from government bonds’ portfolio held by Polish banks. Adequacy of VaR measures counted with particular methods is compared with the help of formalized criteria and best fitted methodology is recommended.

9

Axiomatic extension of risk measurement

94%

Khemissi E.

Econometrics. Ekonometria. Advances in Applied Data Analytics

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2017

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issue 2 (56)

116-126

EN

In the article the author introduce the additional axiom of measure of risk and checks, mathematically proving, which well-known functions of risk fulfill this additional axiom. This will be conducted for functions such as: Value at Risk, Expected Shortfall, Median, Absolute Median Deviation, Maximum, Maximum Loss, Half Range, and Arithme- tic Average. In other words, the purpose of the paper is studying which of the above func- tions fulfill the additional axiom of measure of risk, which can enrich Arzner’s and other axioms. This axiom is not a consequence of Arzner’s and other axioms. Furthermore, the author researches mathematically if the mentioned functions of risk retain their properties after replacing the partial order with the stochastic order. Finally the author presents the new measure of risk which fulfills all the axioms of measure of risk and the additional axiom.

10

The use of Value-at-Risk methodology in the assessment of investor’s risk attitudes on the precious metals market

83%

Krężołek D.

Econometrics. Ekonometria. Advances in Applied Data Analytics

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2017

|

issue 3 (57)

101-112

EN

The decision making process is directly associated with risk, no matter what area of interest it is. In the case of financial investments we can define a special type of risk called investment risk. Taking into account the financial time series of assets’ characteristics (prices, returns), small deviations of future values comparing to their expected level are not a major threat to the investor’s portfolio. In contrast, if the changes in prices/returns are significant, unpredictable and result from unexpected and adverse events, one should pay attention to the proper risk measurement. The topic of this article refers to the new family of risk measures related to investments in assets on the precious metals market. These risk measures are called the GlueVaR risk measures. The name itself suggests that the GlueVaR is related to the commonly used measure of risk – VaR. As will be presented in the article, the family of the GlueVaR risk measures may be expressed as a linear combination of VaR and conditional VaR for fixed tolerance levels. Moreover, the new risk measure allows for assessing risk more personally, taking into account the investor’s attitudes towards risk. If portfolio investments are of interest, the GlueVaR risk measures meet the assumption of subadditivity. This property of risk measure is required, as it is strongly related to the diver-sification problem.

11

The Gluevar Risk Measure and Investor’s Attitudes to Risk–An Application to the Non-Ferrous Metals Market

83%

Krężołek D.

Statistics in Transition new series

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2016

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vol. 17

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issue 2

305-316

EN

Investing in the economic world, characterized by a high level of uncertainty and volatility, entails a higher level of risk related to investment. One of the most commonly used risk measure is Value-at-Risk. However, despite the ease of calculation and interpretation, this measure suffers from a significant drawback – it is not subadditive. This property is the key issue in terms of portfolio diversification. Another risk measure, which meets this assumption, has been proposed – Conditional Value-at-Risk, defined as a conditional loss beyond Value-at-Risk. However, the choice of a risk measure is an individual decision of an investor and it is directly related to his attitudes to risk. In this paper the new risk measure is proposed – the GlueVaR risk measure, which can be defined as a linear combination of VaR and GlueVaR. It allows for calculating the level of investment loss depending on investment’s attitudes to risk. Moreover, GlueVaR meets the subadditivity property, therefore it may be used in portfolio risk assessment. The application of the GlueVaR risk measure is presented for the non-ferrous metals market.

12

Expected shortfall and Harell-Davis estimators of value-at-risk

83%

Gadomski L., Glavan V.

Metody Ilościowe w Badaniach Ekonomicznych

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2010

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vol. 11

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issue 1

81-89

EN

The most widely used estimator for the Value-at-Risk is the corresponding order statistic. It relies on a single historic observation date, therefore it can exhibit high variability and provides little information about the distribution of losses around the tail. In this paper we purpose to replace this estimator of VaR by an appropriately chosen estimator of the Expected Shortfall. We also consider the Harrel-Davis estimator of VaR and give some comparative analysis among these estimators.

13

Combining forecasts? Keep it simple

83%

Lis S., Chlebus M.

Central European Economic Journal

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2023

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vol. 10

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issue 57

343-370

EN

This study contrasts GARCH models with diverse combined forecast techniques for Commodities Value at Risk (VaR)modeling, aiming to enhance accuracy and provide novel insights. Employing daily returns data from 2000 to 2020 forgold, silver, oil, gas, and copper, various combination methods are evaluated using the Model Confidence Set (MCS) procedure. Results show individual models excel in forecasting VaR at a 0.975 confidence level, while combined methods outperform at 0.99 confidence. Especially during high uncertainty, as during COVID-19, combined forecasts prove more effective. Surprisingly, simple methods such as mean or lowest VaR yield optimal results, highlighting their efficacy. This study contributes by offering a broad comparison of forecasting methods, covering a substantial period, and dissecting crisis and prosperity phases. This advances understanding in financial forecasting, benefiting both academia and practitioners.

14

Comparative analysis of sigma-based, quantile-based and time series VaR estimators

82%

Małecka M.

Acta Universitatis Lodziensis. Folia Oeconomica

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2015

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vol. 1

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issue 311

PL

Od czasu wprowadzenia VaR pod koniec XX wieku, miara ta stała się najpopularniejszą miarą ryzyka. Jako główne jej zalety uznaje się: łatwość interpretacji, możliwość uzyskania syntetycznej informacji o poziomie ryzyka w postaci jednaj liczby oraz porównywalność poziomów ryzyka raportowanych przez różne instytucje. Jednak możliwość porównywania poziomów ryzyka pozostaje w sprzeczności z faktem stosowania różnych procedur wyznaczania tej miary. Wybór metody estymacji jest wewnętrzną decyzją przedsiębiorstwa i nie podlega regulacjom międzynarodowego nadzoru bankowego. Praca poświęcona została analizie porównawczej błędów estymatora związanych z konkurencyjnymi metodami szacowania VaR. Za pomocą badania Monte Carlo porównano cztery metody, wśród których wybrano dwie oparte na założeniu stacjonarności rozkładu – metodę wariancji-kowariancji oraz symulacji historycznej – oraz dwie metody szeregów czasowych – GARCH i RiskMetricsTM. Analiza porównawcza została przeprowadzona ze względu na wybór metody estymacji, długość szeregu czasowego oraz poziom tolerancji VaR.Wyniki badania pokazały przewagę estymatorów VaR opartych na wariancji nad kwantylową metodą symulacji historycznej. Ponadto porównanie estymatorów opartych na założeniu stacjonarności z estymatorami wywodzącymi się z metod szeregów czasowych pokazało, że uwzględnienie zmienności parametrów pozwoliło na znaczącą redukcję obciążenia i wariancji estymatorów.

EN

Since its inception at the end of the XX century, VaR risk measure has gained massive popularity. It is synthetic, easy in interpretation and offers comparability of risk levels reported by different institutions. However, the crucial idea of comparability of reported VaR levels stays in contradiction with the differences in estimation procedures adopted by companies. The issue of the estimation method is subject to the internal company decision and is not regulated by the international banking supervision. The paper was dedicated to comparative analysis of the prediction errors connected with competing VaR estimation methods. Four methods, among which two stationarity-based – variance-covariance and historical simulation – and two time series methods – GARCH and RiskMetricsTM – were compared through the Monte Carlo study. The analysis was conducted with respect to the method choice, series length and VaR tolerance level.The study outcomes showed the superiority of the sigma-based method of variance-covariance over the quantile-based historical simulation. Furthermore the comparison of the stationarity-based estimates to the time series results showed that allowing for time-varying parameters in the estimation technique significantly reduces the estimator bias and variance.

15

Investment Risk Measurement Based on Quantiles and Expectiles

82%

Trzpiot G.

Acta Universitatis Lodziensis. Folia Oeconomica

|

2018

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vol. 5

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issue 338

213-227

PL

W badaniach starano się przyjrzeć szczegółowemu pomiarowi ryzyka inwestycyjnego. Użyto regresji kwantylowej jako modelu, opisując bardziej ogólne właściwości rozkładu stopy zwrotu. W regresji kwantylowej przyjęto efekty regresji względem warunkowych kwantyli regresorów. W modelu regresji skoncentrowano się na rozszerzeniu regresji liniowej (OLS), wykorzystując regresję oczekiwań. Celem zastosowania obu podejść jest pomiar ryzyka inwestycyjnego. Obydwa modele regresji są wersją ważonego modelu najmniejszych kwadratów. Najczęściej stosowanymi rodzinami miar ryzyka, poza miarami zmienności, są miary zagrożenia, a w praktyce wartość zagrożona (VaR) i warunkowa wartość zagrożona ryzykiem (CVaR). Można je oszacować przez kwantyle lub oczekiwania wyznaczone w ogonie rozkładu odpowiedzi.

EN

In the presented research, we attempt to examine special investment risk measurement. We use quantile regression as a model by describing more general properties of the response distribution. In quantile regression, we assume regression effects on the conditional quantile function of the response. In regression modelling, the focus is on extending linear regression (OLS), and in this paper we seek to apply expectile regression. The purpose of using both approaches is investment risk measurement. Both regression models are a version of least weighted squares model. The families of risk measures most commonly used in practice are the Value‑at‑Risk (VaR) and the Conditional Value‑at‑Risk (CVaR), which can be estimated by quantiles or expectiles in the tail of the response distribution.

16

Portfolio selection: method of the step by step assigned weights

71%

Pavlík M., Michalski G., Lukáčik M.

Econometrics. Ekonometria. Advances in Applied Data Analytics

|

2015

|

issue 3 (49)

78-97

EN

The authors conceived a new simple method for creating the approximation of the border of investment opportunities. The method enumerates all the possibilities of assigning weights to the investment portfolio. It does not enable short sales. The software which the authors coded is written in VBA and also enables active management. The method is simple, accurate but demanding. The authors also created a simple methodology for testing the quality of the approximation of the border of investment opportunities.

17

Estimating Model Risk of VaR under Different Approaches: Study on European Banks

71%

Pasieczna A. H., Szydłowska M. J.

Współczesne Problemy Zarządzania

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2021

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vol. 9

|

issue 2(19)

65-76

EN

The objective of this research is to estimate the model risk, represented as precision, and the accuracy of the Value at Risk (VaR) measure, under three different approaches: historical simulation (HS), Monte Carlo (MC), and generalized ARCH (GARCH). In this work, to analyze the VaR model, the accuracy and precision were used. Estimation of the accuracy and precision was done under the three approaches for four European banks at 95 and 99% confidence levels. The percentage crossings and Kupiec POF were used to judge the model accuracy, whereas the ratio of the maximum and minimum VaR estimates, and the spread between the maximum and minimum VaR estimates were used to estimate the model risk. This was achieved by changing input parameters, specifically, the estimation time window (125, 250, 500 days). Implications/Recommendations: The accuracy alone is not sufficient to evaluate a model and precision is also required. The temporal evolution of the precision metrics showed that the VaR approaches were inconsistent under different market conditions. This article focuses on the accuracy and precision concepts applied to estimate model risk of the Value at Risk (VaR). VaR is the foundation for sophisticated risk metrics, including systemic risk measures like Marginal Expected Shortfall and Delta Conditional Value at Risk. Thus, understanding the risk associated with the use of VaR is crucial for finance practitioners.

18

Zmienność cen na globalnym rynku surowców a ryzyko banku

67%

Włodarczyk B.

Problemy Zarządzania

|

2017

|

issue 1/2017 (66), t.2

EN

Price volatility in raw material markets significantly affects the efficiency of real economy. Raw materials are not only used in the industry but are also very popular in periods of economic downturn. An appropriate prognosis of price volatility in these markets and their adequate security ensured by means of financial instruments can be a basis for avoiding many financial perturbations of enterprises, and consequently of financial institutions. Financial institutions, including banks, are exposed to credit and market risk, through the absorption of a part of market risk in a direct (investments in raw materials, transaction services) and indirect way (providing credit to entities in commodity markets). Selection of these prognosis tools as well as appropriate instruments securing prices, hence hedging the risk from the financial market, are elements of the risk hedging policy in the real sphere, which has an effect on the credit risk and investment. The aim of the article is the bank’s risk assessment in the context of price volatility in commodity markets. At the same time, the research problem was raised that refers to the way in which the variability of prices and rates of return in the commodity market is reflected in the level of the bank’s risk. An analysis of the asymmetry effect and long memory in the modelling and prognosis of conditional volatility and market risk on the commodity market was conducted in the article, taking petroleum as an example. GARCH and FIAPARCH models were used for that purpose. The analysis of the in-sample and out-of-sample prognosis showed that the variation of rates of return for oil is better described by a non-linear model of the variation using a long memory and asymmetry effect.

PL

W dotychczasowych badaniach zmienności na rynkach towarowych brano pod uwagę dynamikę zmienności cen wybranych towarów lub analizowano przenoszenie się w czasie zmienności z jednych towarów na inne. W tym celu wykorzystywano standardowe modele zmienności. Obecnie w ramach przeprowadzanych badań gromadzi się różnorodne charakterystyki zmienności towarów i ich grup w celu skompletowania metodycznego zestawu narzędzi o większej precyzji prognostycznej. Niestabilność cen na rynkach surowców istotnie wpływa na efektywność sfery realnej gospodarki. Surowce nie tylko są wykorzystane w przemyśle, ale też cieszą się dużym zainteresowaniem inwestorów w okresach dekoniunktury gospodarczej, będąc przedmiotem spekulacji. Można zatem stwierdzić, że oddziaływanie zmienności cen surowców na ryzyko banku opiera się na mechanizmie bezpośrednim (poprzez ryzyko rynkowe) i pośrednim (poprzez ryzyko kredytowe). W artykule zaprezentowano oba ujęcia, przy czym ryzyko rynkowe zostało metodycznie uwypuklone. Odpowiednie wyselekcjonowanie narzędzi prognozowania oraz zastosowanie właściwych instrumentów zabezpieczających to elementy skutecznej polityki zabezpieczeń ryzyka, które kształtują zarówno ryzyko rynkowe (oddziaływanie bezpośrednie), jak i ryzyko kredytowe banków (ujęcie pośrednie).

19

Calculating VaR in EU Candidate States

60%

Žiković S.

South East European Journal of Economics and Business

|

2008

|

vol. 3

|

issue 1

23-33

EN

This paper examines whether VaR models that are created and suited for developed and liquid markets apply to the volatile and shallow financial markets of EU candidate states. To this end, several VaR models are tested on five official stock indexes from EU candidate states over a period of 500 trading days. The tested VaR models are: a historical simulation with rolling windows of 50, 100, 250 and 500 days, a parametric variance-covariance approach, a BRW historical simulation, a RiskMetrics system and a variance-covariance approach using GARCH forecasts. Based on the backtesting results it can be concluded that VaR models that are commonly used in developed financial market are not well-suited to measuring market risk in EU candidate states. Using some of the most widespread VaR models in these circumstances may result in serious problems for both banks and regulators.

20

Experimental Design in Evaluating VaR Forecasts

60%

Małecka M., University of Lodz D. o. S. M.

Acta Universitatis Lodziensis. Folia Oeconomica

|

2013

|

vol. 286

EN

Following a dynamic development of VaR estimation methods from 90s, in recent literature much attention has been paid to testing procedures designed to evaluate quality of VaR models. There has been a wide-ranging discussion on both – statistical properties and empirical application of the two most popular tests, which are Kupiec test from 1995 that considers the ratio of VaR exceedances and Christoffersen autocorrelation test from 1998. We focused on autocorrelation property and compared Christoffersen test to Ljung Box test of 1978 and to the proposition of Engle and Mangianelli from 2004. The goal of the paper was to explore the design of experiments in the context of evaluating power of autocorrelation tests. We presented and contrasted simulation experiments proposed in the literature, indicated their design influence on the results and proposed a new scheme for power evaluating in autocorrelation tests.

PL

W ślad za dynamicznym rozwojem metod estymacji VaR, począwszy od lat dziewięćdziesiątych ubiegłego wieku, w literaturze pojawiła się obszerna dyskusja dotycząca możliwości testowania statystycznego w kontekście oceny modeli VaR. Z jednej strony powstało wiele prac odnoszących się do własności statystycznych dwóch najpopularniejszych testów – testu Kupca z 1995 roku, który bada udział przekroczeń VaR w szeregu i testu autokorelacji przekroczeń VaR Christoffersena z 1998 roku. Z drugiej strony istnieje bogata literatura dotycząca zastosowań rozważanych testów do empirycznych szeregów czasowych. W niniejszej pracy skoncentrowano się na analizie własności testów autokorelacji i porównano test Christoffersena do testów Ljunga Boxa z 1978 roku i testu Engla i Mangianelli’ego z 2004. Celem pracy było przedstawienie przeglądu eksperymentów symulacyjnych wykorzystywanych do badania mocy testów autokorelacji przekroczeń VaR w odniesieniu do założeń metody Monte Carlo oraz zaprezentowanie własnej propozycji eksperymentu.

Refine search results

Porównanie metod estymacji VaR na polskim rynku gazu

Weryfikacja historyczna modeli wartości zagrożonej – zastosowanie wybranych metod dla rynku polskiego w okresie kryzysu finansowego

THE USE OF A VALUE AT RISK MEASURE FOR THE ANALYSIS OF BANK INTEREST MARGINS

Zastosowanie funkcji łączących w wyznaczaniu granic dla Value-at-Risk

ARIMA-GARCH MODELS IN ESTIMATING MARKET RISK USING VALUE AT RISK FOR THE WIG20 INDEX

Modele zmienności w kalkulacjach Value at Risk ocena i dobór modelu

The application of generalized pareto distribution and copula functions in the issue of operational risk

Comparison of Alternative Approaches to VaR Evaluation

Axiomatic extension of risk measurement

The use of Value-at-Risk methodology in the assessment of investor’s risk attitudes on the precious metals market

The Gluevar Risk Measure and Investor’s Attitudes to Risk–An Application to the Non-Ferrous Metals Market

Expected shortfall and Harell-Davis estimators of value-at-risk

Combining forecasts? Keep it simple

Comparative analysis of sigma-based, quantile-based and time series VaR estimators

Investment Risk Measurement Based on Quantiles and Expectiles

Portfolio selection: method of the step by step assigned weights

Estimating Model Risk of VaR under Different Approaches: Study on European Banks

Zmienność cen na globalnym rynku surowców a ryzyko banku

Calculating VaR in EU Candidate States

Experimental Design in Evaluating VaR Forecasts