In this thesis we use the GARCH(1,1) and GJR-GARCH(1,1) models to estimate the conditional variance for five equities from the OMX Nasdaq Stockholm (OMXS) stock exchange. We predict 95% and 99% Value-at-Risk (VaR) using one-day ahead forecasts, under three different error distribution assumptions, the Normal, Student’s t and the General Error Distribution. A 500 observations rolling forecast-window is used on the dataset of daily returns from 2007 to 2014. The empirical size VaR is evaluated using the Kupiec’s test of unconditional coverage and Christoffersen’s test of independence in order to provide the most statistically fit model. The results are ultimately filtered to correspond with the Basel (II) Accord Penalty Zones to present the preferred models. The study finds that the GARCH(1,1) is the preferred model when predicting the 99% VaR under varying distribution assumptions.

The measurement of operational risk has surely been one of the biggest challenges for banks worldwide. Most banks worldwide have opted for a value-at-risk (VaR) approach, based on the success achieved with market risk, to measure and quantify operational risk. The problem banks have is that they do not always find it difficult to calculate this VaR figure, as there are numerous mathematical and statistical methods and models that can calculate VaR, but they struggle to understand and interpret the values that are produced by VaR models and methods. Senior management and normal staff do not always understand how these VaR values will impact their decision-making and they do not always know how to incorporate these values in their day-to-day management of the bank. This study therefore aims to explain and discuss the calculation of VaR for operational risk as well as the factors that influence this figure, and then also to discuss how this figure is managed and the impact that it has on the management of a bank. The main goal of this study is then to explain the management of VaR for operational risk in order to understand how it can be incorporated in the overall management of a bank. The methodology used includes a literature review, in-depth interviews and a case study on a South African Retail Bank to determine and evaluate some of the most renowned methods for calculating VaR for operational risk. The first objective of this study is to define operational risk and all its elements in order to distinguish it from all the other risks the banking industry faces and to better understand the management thereof. It is the view of this study that it will be impossible to manage and measure operational risk if it is not clearly defined, and it is therefore important to have a clear and understandable definition of operational risk. The second objective is to establish an operational risk management process that will ensure a structured approach to the management of operational risk, by focusing on the different phases of operational risk. The process discussed by this study is a combination of some of the most frequent used processes by international banks, and is intended to guide the reader in terms of the steps required for managing operational risk. The third objective of this study is to discuss and explain the qualitative factors that play a role in the management of operational risk, and to determine where these factors fit into the operational risk process and the role they play in calculating the VaR for operational risk. These qualitative factors include, amongst others, key risk indicators (KRIs), risk and control self-assessments and the tracking of operational losses. The fourth objective is to identify and evaluate the quantitative factors that play a role in the management of operational risk, to distinguish these factors from the qualitative factors, and also to determine where these factors fit into the operational risk management process and the role they play in calculating VaR for operational risk. Most of these quantitative factors are prescribed by the Base1 Committee by means of its New Capital Accord, whereby this new framework aims to measure operational risk in order to determine the amount of capital needed to safeguard a bank against operational risk. The fifth objective is to discuss and explain the calculation of VaR for operational risk by means of discussing all the elements of this calculation. This study mainly bases its discussion on the loss distribution approach (LDA), where the frequency and severity of operational loss events are convoluted by means of Monte Carlo simulations. This study uses real data obtained from a South African Retail Bank to illustrate this calculation on a practical level. The sixth and final objective of this study is to explain how VaR for operational risk is interpreted in order for management to deal with it and make proper management decisions based on it. The above-mentioned discussion is predominantly based on the two types of capital that are influenced by VaR for operational risk. / Thesis (Ph.D. (Risk Management))--North-West University, Potchefstroom Campus, 2007.

This essay investigates three different GARCH-models (GARCH, EGARCH and GJR-GARCH) along with two distributions (Normal and Student’s t), which are used to forecast the Value at Risk (VaR) for different return series. Seven major international equity indices are examined. The purpose of the essay is to answer which of the three models that is better at forecasting the VaR and which distribution is more appropriate.  The results show that the EGARCH(1,1)  is preferred for all indices included in the study.

Radio spectrum is scarce in wireless communication. While there is an increasing demand for spectrum due to the substantial growth of wireless communication systems, extensive measurements observe that conventional static spectrum allocation policies introduce significant inefficiency in spectrum utilization. To achieve higher spectrum efficiency, cognitive radio networks have emerged as a revolutionary technology by allowing unlicensed (secondary) users to utilize licensed bands opportunistically without harming licensed (primary) users. In this thesis, we seek to design a new framework that addresses three important issues in cognitive radio networks simultaneously: protection of primary users, incentives for primary networks to share their spectrum and the performance guarantee for secondary users. Leveraging the idea of Value at Risk from economics, in our solution, primary networks maximize their profits by charging secondary users for opportunistic spectrum access, while in the meantime secondary users impose utility constraints to manage the risks and guarantee performance probabilistically.

Radio spectrum is scarce in wireless communication. While there is an increasing demand for spectrum due to the substantial growth of wireless communication systems, extensive measurements observe that conventional static spectrum allocation policies introduce significant inefficiency in spectrum utilization. To achieve higher spectrum efficiency, cognitive radio networks have emerged as a revolutionary technology by allowing unlicensed (secondary) users to utilize licensed bands opportunistically without harming licensed (primary) users. In this thesis, we seek to design a new framework that addresses three important issues in cognitive radio networks simultaneously: protection of primary users, incentives for primary networks to share their spectrum and the performance guarantee for secondary users. Leveraging the idea of Value at Risk from economics, in our solution, primary networks maximize their profits by charging secondary users for opportunistic spectrum access, while in the meantime secondary users impose utility constraints to manage the risks and guarantee performance probabilistically.

Zugl.: Jena, Univ., Diss., 2004

Zürich, Univ., Diss., 2007.

Univ., Diss.--Siegen, 2004. / Literaturverz. S. 293 - 303.

Techn. University, Diss., 2006--München.

Diss. Nr. 2834 Wirtschaftswiss. St. Gallen. / Literaturverz.