O grande número de publicações na área de finanças atualmente utilizando a modelagem de cópulas pode ser explicada pela capacidade de esta técnica estatística conseguir lidar com a evidência de não normalidade das séries de retornos de ativos financeiros. A não normalidade é evidenciada através do “sorriso de volatilidade” presente em séries de opções de ações perto do vencimento; existência de “caudas pesadas” em carteiras de instituições e consequentemente no gerenciamento de risco das Instituições. Particularmente com relação ao Value at Risk (VaR), que é uma técnica estatística que tem por objetivo calcular a perda máxima de uma carteira em dado horizonte de tempo considerando um nível de significância adotado, a existência de caudas pesadas nas séries gera um problema para a determinação da distribuição de probabilidade conjunta, implicando em grande dificuldade na mensuração do grau de exposição aos fatores de risco. Esse fato acaba por dificultar o correto e efetivo gerenciamento de risco de uma carteira, pois em tese, devido à existência de não normalidade, não é possível separar os efeitos de ativos de diferentes características. Em casos de crises e bolhas, o portfólio pode ser mais arriscado que o desejado ou excessivamente conversador. Neste sentido, a utilização de Cópulas torna-se atrativa, pois com esta técnica é possível separar as distribuições marginais de cada ativo da estrutura de dependência das variáveis. O objetivo do trabalho é propor uma modelagem de risco a partir do uso de Cópulas para o cálculo do Value at Risk (VaR), utilizando os métodos de volatilidade GARCH (1,1), EWMA e HAR. A aplicação empírica do modelo foi efetuada a partir de uma amostra de uma série de retornos de uma carteira teórica composta por ativos de renda variável (ações preferenciais) das empresas Petrobras, Vale, Usiminas e Gerdau. A amostra utilizada corresponde aos preços diários entre o período de 03 de março de 2006 até 30 de abril de 2010, representando 1.026 observações diárias. Os resultados apurados para a amostra demonstraram que as cópulas tendem a gerar um Value at Risk (VaR) significativo para a maioria das famílias de Cópulas, quando testado pelo Teste de Kupiec (1995). / The large number of publications in finance using currently copulas can be explained by the ability of this technique to deal with statistical evidence of non-normality of the return series of financial assets. The non-normality is evidenced by the "volatility smile" in the series of stock options near expiration, the existence of "heavy tails" in portfolios of institutions and consequently the risk management of the institutions. Especially regarding the Value at Risk (VaR), which is a statistical technique that aims to calculate the maximum loss a portfolio at a given time horizon considering a significance level, the existence of heavy tails in the series creates a problem for determining the joint probability distribution, resulting in great difficulty in measuring the degree of exposure to risk factors. This fact makes difficult the correct and effective risk management of a portfolio, because in theory, due to the existence of non-normality, it is not possible to separate the effects of assets with different characteristics. In cases of crises and bubbles, the portfolio may be riskier than desired or overly chatty. In this regard, the use of copulas becomes attractive, because with this technique is possible to separate the marginal distributions of each dependence structure of the variables. The objective is to propose a model of risk using copulas for the calculation of Value at Risk (VaR), using the methods of volatility GARCH (1,1), EWMA and HAR. The empirical application of the model was made from a sample of a series of returns of a theoretical portfolio of assets in equities (shares) of Petrobras, Vale, Usiminas and Gerdau. The sample corresponds to the daily prices in the period between March 3rd, 2006 until April 30th, 2010, representing 1026 daily observations. The results obtained showed that copulas tend to generate a Value at Risk (VaR) for the most significant families of copulas, when tested by the Test of Kupiec (1995).

nÃo hà / Este trabalho utiliza a fronteira eficiente desenvolvida no Ãmbito da Teoria Moderna de Carteiras, objetivando atender as peculiaridades do setor e promover uma maior aproximaÃÃo com as prÃticas atuais de finanÃas. Neste sentido, o destaque fica por conta da inclusÃo do conceito de value-at-risk â VaR como instrumento de anÃlise. A verificaÃÃo da eficÃcia do modelo serà realizada tanto de forma qualitativa, atravÃs da discussÃo sobre a carteira eficiente tradicional e a carteira eficiente modificada, quanto no aspecto quantitativo, atravÃs da aplicaÃÃo prÃtica do modelo na Caixa de PrevidÃncia dos FuncionÃrios do Banco do Nordeste do Brasil - CAPEF, Entidade Fechada de PrevidÃncia Complementar patrocinada pelo Banco do Nordeste, pela Caixa de AssistÃncia MÃdica dos FuncionÃrios do Banco do Nordeste e pela prÃpria CAPEF. Tal aplicaÃÃo prÃtica permitirà mostrar a viabilidade da pesquisa dentro da Ãrea de investimentos dos Fundos de PensÃo / This work uses the efficient border developed in the scope of the Modern Wallet Theory, objectifying to take care of the peculiarities of the practical sector and to promote a bigger approach with the current ones of finances. In this direction, the prominence is on account of the inclusion of the concept of value-at-risk - VaR as analysis instrument. The verification of the effectiveness of the model will be carried through in such a way of qualitative form, through the quarrel on the traditional efficient wallet and the modified efficient wallet, how much in the quantitative aspect, through the practical application of the model in the Box of Providence of the Employees of the northeast Bank of Brazil - CAPEF, Closed Entity of Complementary Providence sponsored by the northeast Bank, the Box of Medical Assistance of the Employees of the northeast Bank and by the proper CAPEF. Such practical application will allow to inside show the viability of the research of the area of investments of the Pension funds.

In this thesis, probability theory and risk analysis are used to determine the riskof wind energy stocks. Three stocks of wind energy companies and three stocksof technology companies are gathered and risks are compared. Three difffferent riskmeasures: variance, value at risk, and conditional value at risk are used in this thesis.Conclusions which has been drawn, are that wind energy company stock risks arenot signifificantly lower than the stocks of other companies. Furthermore, optimalportfolios should include short positions of one or two of the energy companies forthe studied time period and under the difffferent risk measures.

Finance risk management has been playing an increasingly important role in the finance sector, to analyse finance data and to prevent any potential crisis. It has been widely recognised that Value at Risk (VaR) is an effective method for finance risk management and evaluation. This thesis conducts a comprehensive review on a number of VaR methods and discusses in depth their strengths and limitations. Among these VaR methods, Monte Carlo simulation and analysis has proven to be the most accurate VaR method in finance risk evaluation due to its strong modelling capabilities. However, one major challenge in Monte Carlo analysis is its high computing complexity of O(n²). To speed up the computation in Monte Carlo analysis, this thesis parallelises Monte Carlo using the MapReduce model, which has become a major software programming model in support of data intensive applications. MapReduce consists of two functions - Map and Reduce. The Map function segments a large data set into small data chunks and distribute these data chunks among a number of computers for processing in parallel with a Mapper processing a data chunk on a computing node. The Reduce function collects the results generated by these Map nodes (Mappers) and generates an output. The parallel Monte Carlo is evaluated initially in a small scale MapReduce experimental environment, and subsequently evaluated in a large scale simulation environment. Both experimental and simulation results show that the MapReduce based parallel Monte Carlo is greatly faster than the sequential Monte Carlo in computation, and the accuracy level is maintained as well. In data intensive applications, moving huge volumes of data among the computing nodes could incur high overhead in communication. To address this issue, this thesis further considers data locality in the MapReduce based parallel Monte Carlo, and evaluates the impacts of data locality on the performance in computation.

Cloud computing at a high level comprises of the availability of hardware, software and technical support via a network protocol to a remote client on a pay-per-use basis. Businesses using Cloud resources has been increasing steadily in the very recent past and the number of Cloud service providers (CSP) are increasing as well. The challenges that characterize a Cloud data center include: on-demand service, elasticity, resources pooling, broad network access, service meters. As the customer base is in creasing and their resource requirement and usage pattern has been becoming highly volatile, proper utilization of the resources and generating revenue by appropriately charging the clients for their uses has become an even more challenging research problem. In other words, Cloud resource pricing has emerged as an important and pressing problem to study for ever increasing utility of Cloud computing. Literature review reveals that there are economy-based models (cash flow, net present value etc.) used for charging mechanism suggested by many researchers. Most of these models are rigid that they are not build with the core of Cloud - elasticity in mind. Also, the economic models do not provide flexibility of the economy of scale to either increase or decrease the resource requirement and appropriately charge for such increase or decrease in resource use. For my thesis, I have designed and developed a Cloud resources pricing model that satisfies two important constraints: the dynamic ability of the model to provide a high satisfaction guarantee measured as Quality of Service (QoS) - from users perspectives, and profitability constraints - from the Cloud service providers perspectives. I have employed financial option theory and treated the Cloud resources as underlying assets to capture the realistic value of the Cloud Compute Commodities (C3). I have priced the Cloud resources using my model. Through this research, I show that the Cloud parameters can be mapped to financial economic model and that this model can be effectively implemented for resource pricing purpose. I discuss the results of pricing Cloud Compute Commodities (C3) for various input parameters, such as the age of the resource and quality of service. / February 2016

The goal of this thesis is to measure the concentration risk of a portfolio as a part of a investment risk considered from the view of insurance companies by various methods and also to compare achieved results. Concentration risk in credit portfolios originates in uneven distribution of invested funds to individual obligors and it is important to manage it. In the theoretical part there are two methods presented - one is being used in practice CreditMetrics), the other one, the EU Directive, will be put into effect in the near future (Solvency II). In the practical part the methods are applied on model portfolios and the results are compared in order to decide how the methods reflect the concentration risk.

Despite its recent advent, value at risk (VaR) became the most widely used technique for measuring future expected risk for both financial and non-financial institutions. VaR, the measure of the worst expected loss over a given horizon at a given confidence level, depends crucially on the distributional aspects of trading revenues. Existing VaR models do not capture adequately some empirical aspects of financial data such as the tail thickness, which is vital in VaR calculations. Tail thickness in financial variables results basically from stochastic volatility and event risk (jumps). Those two sources are not totally separated; under event risk, volatility updates faster than under normal market conditions. Generally, tail thickness is associated with hyper volatility updating. Existing VaR literature accounts partially for tail thickness either by including stochastic volatility or by including jump diffusion, but not both. Additionally, this literature does not account for fast updating of volatility associated with tail thickness. This dissertation fills the gap by developing analytical VaR models account for the total (maximum) tail thickness and the associated fast volatility updating. Those aspects are achieved by assuming that trading revenues are evolving according to a mixed non-affine stochastic volatility-jump diffusion process. The mixture of stochastic volatility and jumps diffusion accounts for the maximum tail thickness, whereas the nonaffine structure of stochastic volatility captures the fast volatility updating. The non-affine structure assumes that volatility dynamics are non-linearly related to the square root of current volatility rather than the traditional linear (affine) relationship. VaR estimates are obtained by deriving the conditional characteristic function, and then inverting it numerically via the Fourier Inversion technique to infer the cumulative distribution function. The application of the developed VaR models on a sample that contains six U.S banks during the period 1995-2002 shows that VaR models based on the non-affine stochastic volatility and jump diffusion process produce more reliable VaR estimates compared with the banks' own VaR models. The developed VaR models could significantly predict the losses that those banks incurred during the Russian crisis and the near collapse of the LTCM in 1998 when the banks' VaR models fail.

Thesis (Ph.D. (Risk Management))--North-West University, Potchefstroom Campus, 2007.

Ce travail se compose de trois parties consacrées à différents aspects des modèles ARCH (AutoRegressive Conditionally Heteroskedastic) quantiles. Dans ces modèles, l’hétéroscédasticité conditionnelle est à prendre dans un sens très large, et affecte de fa¸ con potentiellement différenciée tous les quantiles conditionnels (et donc la loi conditionnelle elle-même), et non seulement, comme dans les modèles ARCH classiques, l’échelle conditionnelle. La première partie étudie les problèmes de Value-at-Risk (VaR) dans les séries financières ainsi modélisées. Les approches traditionnelles présentent une caractéristique discutable, que nous relevons, et à laquelle nous apportons une correction fondée sur les lois résiduelles. Nous pensons que les fondements de cette nouvelle approche sont plus solides, et permettent de prendre en compte le fait que le comportement des processus empiriques résiduels (REP) des processus ARCH, contrairement à celui des REP des processus ARMA, continue à dépendre de certains des paramètres du modèle. La seconde partie approfondit l’étude générale des processus empiriques résiduels (REP) des processus ARCH dans l’optique de la régression quantile (QR) au sens de Koenker et Bassett (Econometrica 1978). La représentation de Bahadur des estimateurs QR, et dont découle la propriété de tension asymptotique des REP, est établie. Finalement, dans la troisième partie, nous mettons en évidence la nature semi-paramétrique des modèles ARCH quantiles, et l’invariance, sous l’action de certains groupes de transforma-tions, des sous-modèles obtenus en fixant la valeur des paramètres. Cette structure de groupe permet la construction de méthodes d’inférence invariantes qui, dans l’esprit des résultats de Hallin and Werker (Bernoulli 2003) préservent l’optimalité au sens semi-paramétrique. Ces méthodes sont fondées sur les rangs et les signes résiduels. Nous développons en particulier les R-estimateurs des modèles considérés et étudions leurs performances.

Following the Basel Committee’s advocacy of value-at-risk (VaR) disclosure in external reports of financial institutions, the U.S. Securities and Exchange Commission issued Financial Reporting Release No. 48 to permit VaR disclosure as one of the most important disclosure approaches for market-risk quantitative information in 1997. This study is the first to empirically examine both economic determinants and consequences of VaR disclosure informativeness in the banking industry. First, this study finds that more informative VaR disclosure is associated with more effective corporate governance characteristics, including better shareholder protection, a larger and more independent board, the presence of a separate risk committee under the board of directors, a more independent risk committee, higher institutional ownership and a better overall governance environment. These results suggest that corporate governance mechanisms are important determinants of the informativeness of VaR disclosure. Second, the evidence shows that the cost of equity capital is negatively associated with the informativeness of VaR disclosure, consistent with informative VaR disclosure effectively communicating private information to investors about a bank’s market risk exposure and its risk management system. Additional evidence during the recent crisis further suggests the importance of VaR disclosure informativeness to the capital market as a strong signal reflecting the efficacy of risk management practices and the quality of risk governance mechanisms. However, I still find that a large proportion of the sample banks choose not to disclose information with respect to some important disclosure items (e.g., quantitative stress-test results, and non-trading portfolio VaR). It is necessary for government regulators to re-consider the current regulation on VaR disclosure in the external reports of the banking industry.