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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.
PL
W badaniu rozpatrzone zostały różne sposoby rejestrowania zdarzeń, takie jak ucinanie i cenzurowanie danych wraz z oceną wpływu, jaki mogą wywierać na wielkość ryzyka szacowanego metodą LDA. Ignorowanie faktycznego ucinania danych w procesie ich rejestracji lub przyjmowanie faktu ucinania jako kompromisu pomiędzy jakością informacji a kosztami ich ewidencji zostały porównane z procesem rejestracji opartym na cenzurowaniu danych. Cenzurowanie pozwala na uzyskanie pełnej informacji o częstości zdarzeń oraz daje możliwość wykorzystania tych częściowych informacji w procesie estymacji. Estymacja parametrów na podstawie danych cenzurowanych, wykorzystywana w innych obszarach, może być jednym z kierunków rozwoju w przypadku ryzyka operacyjnego w instytucjach finansowych.
EN
The study consider different ways to register processes such as truncation and censoring of data together with the impact they may have on LDA method. Ignorance of factual truncation of data in the process of their registration or acceptance of the fact of their being truncated as a compromise between the quality of information and the cost of their record were compared with the registration process based on the censorship of information. Censoring of data allows one to get complete information about the frequency of events as well as to implement this partial information further in the process of parameter estimation. Estimation of parameters on the basis of data censoring, may be one of the directions of development also in the case of operational risk in financial institutions.
PL
Tematyka artykułu związana jest z problemem kwantyfikacji ryzyka operacyjnego w banku na bazie modelu LDA. Badanie przeprowadzone w artykule ma na celu ocenę skali narażenia na ryzyko operacyjne przy wykorzystaniu teorii wartości ekstremalnych w celu modelowania prawego ogona rozkładu dotkliwości strat. Artykuł porusza także problem dywersyfikacji ryzyka przy uwzględnieniu zależności pomiędzy różnymi przekrojami analitycznymi za pomocą funkcji copula. Podejście takie motywowane jest przeciwstawnymi propozycjami Komitetu Bazylejskiego ds. Nadzoru Finansowego pole-gającymi na sumowaniu indywidualnych wielkości VaR z poszczególnych przekrojów analitycznych. Wyniki prezentowane w pracy pozwalają na ocenę wpływu ekstremalnych zdarzeń na wielkość miary VaR szacowanej dla dwóch przekrojów analitycznych.
EN
The subject of the article is related to quantification of operational risk in a bank on the basis of LDA model. The study carried out in the article aims at evaluation of the scale of operational risk with the use of theory of extreme values in modelling the right tail of loss severity distribution. The article deals also with the problem of risk diversification with the consideration of dependences among various analytical sections by means of copula functions. Such an approach is motivated by contrary suggestions of Basel Commitee in terms of Financial Supervision which consist in summing up indi-vidual Values at Risk out of particular analytical sections. The conclusions presented in the article allow to evaluate the influence of extreme events on VaR estimated for two analytical sections.
EN
The article presents the method of constructing an econometric model of employment on the basis of expert research, for the need of determining long-term forecasts. In classical models, based merely on the historical data, it is often impossible to consider non-standard factors that may influence the forecasts of values. The lack of historical information regarding events that may occur in the future with a specified probability extorts the application of non-classical methods of estimation of model parameters as well as the correction of forecast values. The methodology adopted in the research included the analysis based on type II formal models and the correction of base forecasts obtained from the initial model with the application of cross effect method as well as the variable trend method in connection with simulation research.
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.
EN
In this paper the authors present a nonparametric method of estimating the parameters of the linear econometric model, which is the method of least absolute deviations (LAD). The aim of this article is to examine the extent to which the parameter estimation method of least absolute deviations is resistant to changes in parameter values in case of outliers. In this paper, a hypothetical example examines the impact of the so-called outliers on the model parameters estimated by OLS methods and LAD respectively. In addition, the work raises the problem of the use of permutation methods MRPP in testing certain statistical hypotheses when the distributions of examined random variables distributions are not normal.
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