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

100%
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.
2
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Assessment of the size of VaR backtests for small samples

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Kaszyński D., Kamiński B., Pankratz B.
Przegląd Statystyczny
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2020
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vol. 67
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issue 2
114-151
EN
The market risk management process includes the quantification of the risk connected with defined portfolios of assets and the diagnostics of the risk model. Value at Risk (VaR) is one of the most common market risk measures. Since the distributions of the daily P&L of financial instruments are unobservable, literature presents a broad range of backtests for VaR diagnostics. In this paper, we propose a new methodological approach to the assessment of the size of VaR backtests, and use it to evaluate the size of the most distinctive and popular backtests. The focus of the paper is directed towards the evaluation of the size of the backtests for small-sample cases – a typical situation faced during VaR backtesting in banking practice. The results indicate significant differences between tests in terms of the p-value distribution. In particular, frequency-based tests exhibit significantly greater discretisation effects than duration-based tests. This difference is especially apparent in the case of small samples. Our findings prove that from among the considered tests, the Kupiec TUFF and the Haas Discrete Weibull have the best properties. On the other hand, backtests which are very popular in banking practice, that is the Kupiec POF and Christoffersen’s Conditional Coverage, show significant discretisation, hence deviations from the theoretical size.
3
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Review of Value at Risk estimation methods

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Stefaniak R.
Prace Naukowe Uniwersytetu Ekonomicznego we Wrocławiu
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2018
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issue 519
173-183
XX
On a daily basis, managers in risk management teams use a number of methods to manage various types of risk. One of the most popular methods of measuring market risk is Value at Risk. Estimation of Value at Risk gives a possibility to determine a loss, which can occur or can be exceeded with a given probability and tolerance level. Moreover, this measure of risk shows in just one number entire risk of the portfolio. In addition, various methods and probability distributions can be used to estimate Value at Risk. A goal of this paper is the evaluation of Value at Risk estimation methods on the basis of backtesting results. In the empirical part, the data for 4 investment portfolios was used. The portfolios were diversified in terms of geographic location of firms that were taken into consideration.
4
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Backtesting analysis. How to assess the quality of PD models in a retail banking

75%
Siarka P.
Prace Naukowe Uniwersytetu Ekonomicznego we Wrocławiu
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2019
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issue vol. 63, nr 8
230-244
EN
The paper refers to the probability of default model validation procedure in retail banking. The author presents the idea of backtesting analysis focusing on sensitivity analysis of capital requirements under stress scenarios. The paper addresses statistical methods which can be applied in credit risk management under the backtesting exercise in retail banking. The advantages and drawbacks of specific approaches are discussed. Furthermore, the outcomes of the empirical implementation of selected methods are presented. The author considers the impact of positive asset correlation on various validation approaches, where no correlation is assumed, and proves that the zero-correlation assumptions may result in a more prudent approach. This finding was confirmed by the empirical analysis performed for retail portfolios. The research concerned PD parameters calculated for car and mortgage loans. The backtesting results revealed that PD forecasts created for mortgage portfolios underestimated credit risk during the crisis period which started in 2008. However, car loan portfolio credit risk predictions appeared to be robust.
PL
W niniejszym artykule odniesiono się do zagadnienia weryfikacji jakości modeli służących do szacowania prawdopodobieństwa niewypłacalności w bankowości detalicznej. Autor przedstawił koncepcję analizy backtesting w świetle wrażliwości wymogów kapitałowych w odniesieniu do testowania warunków skrajnych. W artykule odniesiono się do zagadnienia weryfikacji jakości prognoz modeli służących do szacowania prawdopodobieństwa niewypłacalności. Przedstawiono i omówiono wyniki wybranych metod. Autor omówił również wpływ dodatniej korelacji aktywów na uzyskane wyniki. Wykazał, że założenie zerowej korelacji może skutkować bardziej konserwatywnymi wynikami. Ustalenie to potwierdzono przez analizę empiryczną przeprowadzoną dla portfeli detalicznych. Badanie dotyczyło parametrów PD szacowanych dla portfeli kredytów samochodowych oraz hipotecznych. Otrzymane wyniki wykazały, że prognozy PD opracowane dla portfela kredytów hipotecznych niedoszacowują ryzyko kredytowe. Prognozy ryzyka kredytowego dla portfela kredytów samochodowych okazały się trafne.
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