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Interest rate risk measurement and management in theory and practise
Stará, Pavla ; Pečená, Magda (advisor) ; Patáková, Magdalena (referee)
The bachelor thesis is focused on the risk management in a bank, notably, on the interest rate risk measurement and management. For banks it is important to know the level of risk exposure and according to that to select appropriate management strategy that will minimize adverse fluctuations in bank's profitability. The thesis summarizes the basic models used for measurement, whereas we find out that none of them is perfect and their functionality is conditional upon various assumptions. Furthermore, it deals with analyzing selected basic instruments used for interest rate risk management, which implies that the management process is complex. The usage of various instruments may expose the bank to additional risks. Therefore, it is not possible under the effort to successful management to focus exclusively on the interest rate risk, however, it is necessary to analyze the other risks at the same time. The case study is aimed at the estimation of interest rate risk exposure on the basis of provided GAP analysis. There are three calculation methods presented, although the third one was not possible to apply due to lack of data. Regarding that the obtained results contain just estimates, the final calculations might be affected.
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The use of coherent risk measures in operational risk modeling
Lebovič, Michal ; Teplý, Petr (advisor) ; Doležel, Pavel (referee)
The debate on quantitative operational risk modeling has only started at the beginning of the last decade and the best-practices are still far from being established. Estimation of capital requirements for operational risk under Advanced Measurement Approaches of Basel II is critically dependent on the choice of risk measure, which quantifies the risk exposure based on the underlying simulated distribution of losses. Despite its well-known caveats Value-at-Risk remains a predominant risk measure used in the context of operational risk management. We describe several serious drawbacks of Value-at-Risk and explain why it can possibly lead to misleading conclusions. As a remedy we suggest the use of coherent risk measures - and namely the statistic known as Expected Shortfall - as a suitable alternative or complement for quantification of operational risk exposure. We demonstrate that application of Expected Shortfall in operational loss modeling is feasible and produces reasonable and consistent results. We also consider a variety of statistical techniques for modeling of underlying loss distribution and evaluate extreme value theory framework as the most suitable for this purpose. Using stress tests we further compare the robustness and consistency of selected models and their implied risk capital estimates...
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Predictive Accuracy of Competing Value-at-Risk Specifications during Crisis: An Application to CEE Financial Markets
Kroutil, Tomáš ; Baruník, Jozef (advisor) ; Seidler, Jakub (referee)
The recent worldwide Financial Crisis has increased the need for reliable financial risk measurement and management. In this thesis we evaluate and compare the accuracy of one-day-ahead out-of-sample forecasts of various Value-at-Risk models through a comprehensive assessment framework using crisis data of three CEE stock market indices (PX, WIG20 and BUX) and two benchmark stock indices (S&P 500, DAX). For building the VaR specifications we employ several GARCH extensions allowing either for asymmetry in volatility such as EGARCH, TGARCH and APARCH or long memory like FIGARCH and HYGARCH. Apart from conditional heteroscedasticity models, we also utilize realized volatility estimated by long memory ARFIMA and HAR. Individual volatility models are combined with full parametric approach, filtered historical simulation or filtered extreme value theory. This thesis shows that while VaR specifications based on logarithmic realized volatility, TGARCH and APARCH perform best overall, the benchmark - RiskMetrics model - is not significantly outperformed. The best performing model proves to be the TGARCH-t FHS, which is a combination of asymmetric and heavy-tailed GARCH filter with a historical simulation based approach. Keywords: Value-at-Risk, realized volatility, GARCH extensions, quantile modeling,...
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Sparse robust portfolio optimization via NLP regularizations
Branda, Martin ; Červinka, Michal ; Schwartz, A.
We deal with investment problems where we minimize a risk measure\nunder a condition on the sparsity of the portfolio. Various risk measures\nare considered including Value-at-Risk and Conditional Value-at-Risk\nunder normal distribution of returns and their robust counterparts are\nderived under moment conditions, all leading to nonconvex objective\nfunctions. We propose four solution approaches: a mixed-integer formulation,\na relaxation of an alternative mixed-integer reformulation and\ntwo NLP regularizations. In a numerical study, we compare their computational\nperformance on a large number of simulated instances taken\nfrom the literature.
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