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

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.

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.

Dissertação (mestrado)—Universidade de Brasília, Instituto de Ciências Exatas, Departamento de Estatística, 2015. / Submitted by Fernanda Percia França (fernandafranca@bce.unb.br) on 2016-03-22T19:46:38Z No. of bitstreams: 1 2015_YuriSampaioMaluf.pdf: 4291479 bytes, checksum: 4a9954a7905294836d257652f0ce1753 (MD5) / Approved for entry into archive by Marília Freitas(marilia@bce.unb.br) on 2016-05-26T16:30:44Z (GMT) No. of bitstreams: 1 2015_YuriSampaioMaluf.pdf: 4291479 bytes, checksum: 4a9954a7905294836d257652f0ce1753 (MD5) / Made available in DSpace on 2016-05-26T16:30:44Z (GMT). No. of bitstreams: 1 2015_YuriSampaioMaluf.pdf: 4291479 bytes, checksum: 4a9954a7905294836d257652f0ce1753 (MD5) / Neste trabalho, estudamos a formulação da distribuição de funções de variáveis aleatórias contínuas dependentes. O mecanismo de modelagem da dependência é feita via funções cópulas. Dentre os resultados obtidos formulamos a expressão geral da distribuição da soma de n variáveis aleatórias dependentes. Expandimos a abordagem para a distribuição de outras funções de variáveis aleatórias tais como o quociente, produto e uma combinação convexa. Por meio das R-Vines Cópulas, obtivermos também a expressão da soma de n variáveis aleatórias em que cada componente é governada por um processo GARCH. A partir deste resultado, calculamos o Value-at-Risk (VaR) e Expected Shortfalls (ES) da soma dessas variáveis. Em função desta estrutura, as medidas de risco passam a adquirir um comportamento dinâmico. Ao final do trabalho exibimos algumas ilustrações numéricas via simulação de Monte Carlo. Apresentamos também uma aplicação com dados reais provenientes de bolsas de valores da América Latina. / In this thesis, we studied the distribution of function of dependents continuous random variables. The modeling dependencies structures are made via copula functions. We obtain the general expression of the distribution of the sum of n dependents random variables. This approach is expanded for other functions such as ratio, product and a convex combination. Using R-Vines Copulas, we also derive an expression of the sum of n dependents random variables, being each component governed by AR-GARCH process. From these results, we assess the Value-at-Risk (VaR) and Expected Shortfalls (ES) of the sum of these variables. According to this structure, the VaR takes a dynamic behavior. At the end of this thesis, we show some numerical illustrations via Monte Carlo simulation. An application with real data from Latin American stock markets is also presented.

As entidades fechadas de previdência complementar (EFPC) possuem significativa relevância na economia brasileira com seus ativos dos fundos de pensão representando 16,8% do PIB em dezembro de 2009. O sistema de gerenciamento de risco dos fundos de pensão ainda não evoluiu na mesma proporção em que evoluiu em outros segmentos do mercado financeiro brasileiro. Para atender suas demandas de gerenciamento de risco, os fundos de pensão têm utilizado os modelos propostos para as instituições financeiras; tais modelos, contudo, não chegam a atender integralmente às suas necessidades. Os órgãos reguladores do setor têm estimulado os fundos de pensão a utilizarem seus próprios modelos para estimar a volatilidade e o Value at Risk (VaR). O objetivo do trabalho é propor uma modelagem de risco a partir da volatilidade estocástica (SV) para o cálculo do Value at Risk (VaR), comparando-a com a volatilidade calculada pela EWMA, proposta pelo Risk Metrics . A aplicação empírica do modelo foi efetuada a partir de uma amostra de uma série de retornos da carteira de uma entidade fechada de previdência complementar (EFPC) - fundo de pensão, a Indusprevi - Sociedade de Previdência Privada do Rio Grande do Sul. A amostra utilizada corresponde às cotas diárias entre o período de 01 de abril de 2004 até 31 de dezembro de 2009, representando 1.439 observações diárias. Os resultados apurados para a amostra demonstraram que a volatilidade estocástica (SV) tende a gerar um Value at Risk (VaR) mais conservador que o calculado a partir da metodologia do EWMA, quando testado pelo Teste de Kupiec (1995) e pela realização de Back testing. Tal fato, no entanto, torna o modelo mais adequado à realidade da Indusprevi e de uma grande maioria de outros fundos, que tendem a adotar políticas de investimentos mais conservadoras. / Pension funds have significant relevance to the Brazilian economy with assets representing, in December 2009, 16.8% of GDP. The pension funds risk management system has not evolved in the same pace as other sectors of the Brazilian financial market. To meet their demands for risk management, pension funds have employed the models proposed for financial institutions. Such models, however, fail to fully satisfy their needs. Government regulators have encouraged pension funds to use their own models so as to estimate volatility and Value at Risk (VaR). The main objective of this thesis is to propose a model of risk based on stochastic volatility (SV) to calculate the Value at Risk (VaR), as well as comparing it with the volatility estimated by EWMA, proposed by Risk MetricsTM. The empirical application of the model was made on a sample of portfolio returns of the pension fund Indusprevi - Sociedade de Previdência Privada do Rio Grande do Sul. The sample comprises 1439 daily quotes during the period April 1, 2004 to December 31, 2009. The results showed that the stochastic volatility (SV) tends to generate a more conservative Value at Risk (VaR) than the EWMA method when applying both the Kupiec (1995) test and back testing. This fact, therefore, makes the model more suitable to the principles of Indusprevi as well as a large majority of other funds, which tend to adopt more conservative investment policies.

As entidades fechadas de previdência complementar (EFPC) possuem significativa relevância na economia brasileira com seus ativos dos fundos de pensão representando 16,8% do PIB em dezembro de 2009. O sistema de gerenciamento de risco dos fundos de pensão ainda não evoluiu na mesma proporção em que evoluiu em outros segmentos do mercado financeiro brasileiro. Para atender suas demandas de gerenciamento de risco, os fundos de pensão têm utilizado os modelos propostos para as instituições financeiras; tais modelos, contudo, não chegam a atender integralmente às suas necessidades. Os órgãos reguladores do setor têm estimulado os fundos de pensão a utilizarem seus próprios modelos para estimar a volatilidade e o Value at Risk (VaR). O objetivo do trabalho é propor uma modelagem de risco a partir da volatilidade estocástica (SV) para o cálculo do Value at Risk (VaR), comparando-a com a volatilidade calculada pela EWMA, proposta pelo Risk Metrics . A aplicação empírica do modelo foi efetuada a partir de uma amostra de uma série de retornos da carteira de uma entidade fechada de previdência complementar (EFPC) - fundo de pensão, a Indusprevi - Sociedade de Previdência Privada do Rio Grande do Sul. A amostra utilizada corresponde às cotas diárias entre o período de 01 de abril de 2004 até 31 de dezembro de 2009, representando 1.439 observações diárias. Os resultados apurados para a amostra demonstraram que a volatilidade estocástica (SV) tende a gerar um Value at Risk (VaR) mais conservador que o calculado a partir da metodologia do EWMA, quando testado pelo Teste de Kupiec (1995) e pela realização de Back testing. Tal fato, no entanto, torna o modelo mais adequado à realidade da Indusprevi e de uma grande maioria de outros fundos, que tendem a adotar políticas de investimentos mais conservadoras. / Pension funds have significant relevance to the Brazilian economy with assets representing, in December 2009, 16.8% of GDP. The pension funds risk management system has not evolved in the same pace as other sectors of the Brazilian financial market. To meet their demands for risk management, pension funds have employed the models proposed for financial institutions. Such models, however, fail to fully satisfy their needs. Government regulators have encouraged pension funds to use their own models so as to estimate volatility and Value at Risk (VaR). The main objective of this thesis is to propose a model of risk based on stochastic volatility (SV) to calculate the Value at Risk (VaR), as well as comparing it with the volatility estimated by EWMA, proposed by Risk MetricsTM. The empirical application of the model was made on a sample of portfolio returns of the pension fund Indusprevi - Sociedade de Previdência Privada do Rio Grande do Sul. The sample comprises 1439 daily quotes during the period April 1, 2004 to December 31, 2009. The results showed that the stochastic volatility (SV) tends to generate a more conservative Value at Risk (VaR) than the EWMA method when applying both the Kupiec (1995) test and back testing. This fact, therefore, makes the model more suitable to the principles of Indusprevi as well as a large majority of other funds, which tend to adopt more conservative investment policies.

As entidades fechadas de previdência complementar (EFPC) possuem significativa relevância na economia brasileira com seus ativos dos fundos de pensão representando 16,8% do PIB em dezembro de 2009. O sistema de gerenciamento de risco dos fundos de pensão ainda não evoluiu na mesma proporção em que evoluiu em outros segmentos do mercado financeiro brasileiro. Para atender suas demandas de gerenciamento de risco, os fundos de pensão têm utilizado os modelos propostos para as instituições financeiras; tais modelos, contudo, não chegam a atender integralmente às suas necessidades. Os órgãos reguladores do setor têm estimulado os fundos de pensão a utilizarem seus próprios modelos para estimar a volatilidade e o Value at Risk (VaR). O objetivo do trabalho é propor uma modelagem de risco a partir da volatilidade estocástica (SV) para o cálculo do Value at Risk (VaR), comparando-a com a volatilidade calculada pela EWMA, proposta pelo Risk Metrics . A aplicação empírica do modelo foi efetuada a partir de uma amostra de uma série de retornos da carteira de uma entidade fechada de previdência complementar (EFPC) - fundo de pensão, a Indusprevi - Sociedade de Previdência Privada do Rio Grande do Sul. A amostra utilizada corresponde às cotas diárias entre o período de 01 de abril de 2004 até 31 de dezembro de 2009, representando 1.439 observações diárias. Os resultados apurados para a amostra demonstraram que a volatilidade estocástica (SV) tende a gerar um Value at Risk (VaR) mais conservador que o calculado a partir da metodologia do EWMA, quando testado pelo Teste de Kupiec (1995) e pela realização de Back testing. Tal fato, no entanto, torna o modelo mais adequado à realidade da Indusprevi e de uma grande maioria de outros fundos, que tendem a adotar políticas de investimentos mais conservadoras. / Pension funds have significant relevance to the Brazilian economy with assets representing, in December 2009, 16.8% of GDP. The pension funds risk management system has not evolved in the same pace as other sectors of the Brazilian financial market. To meet their demands for risk management, pension funds have employed the models proposed for financial institutions. Such models, however, fail to fully satisfy their needs. Government regulators have encouraged pension funds to use their own models so as to estimate volatility and Value at Risk (VaR). The main objective of this thesis is to propose a model of risk based on stochastic volatility (SV) to calculate the Value at Risk (VaR), as well as comparing it with the volatility estimated by EWMA, proposed by Risk MetricsTM. The empirical application of the model was made on a sample of portfolio returns of the pension fund Indusprevi - Sociedade de Previdência Privada do Rio Grande do Sul. The sample comprises 1439 daily quotes during the period April 1, 2004 to December 31, 2009. The results showed that the stochastic volatility (SV) tends to generate a more conservative Value at Risk (VaR) than the EWMA method when applying both the Kupiec (1995) test and back testing. This fact, therefore, makes the model more suitable to the principles of Indusprevi as well as a large majority of other funds, which tend to adopt more conservative investment policies.

[pt] Órgãos reguladores internacionais dos setores bancário e securitário têm incentivado a adoção de modelos internos, em apoio ao gerenciamento de riscos, para a determinação de capital mí­nimo regulatório. A maioria dos modelos pode ser decomposta em sub-modelos de determinação de capital para cada tipo de risco que a companhia está exposta. O capital requerido total será a agregação desses capitais individuais. Os riscos de uma companhia podem ter uma interdependância, em geral, não linear, impossibilitando a soma direta desses capitais. Um dos grandes desafios da modelagem é identificar, mensurar e incorporar essas dependências. A teoria de cópulas tem se mostrado uma ferramenta eficaz para agregação dos capitais uma vez que incorpora as estruturas de dependência dos riscos modelados na estimação do capital mínimo. Esta dissertação apresenta uma discussão geral sobre metodologias de mensuração de dependência entre riscos. Estes conceitos são utilizados, no final da dissertação, para a estimação do capital econômico de uma companhia de seguros. Como a cópula nos permite separar os efeitos das estruturas de dependência das caracterí­sticas peculiares às distribuições marginais, é possí­vel explorar o impacto das dependências dos riscos no capital requerido total. A sensibilidade do capital econômico diante do ajuste das cópulas é investigada. As medidas de risco utilizadas para determinar o capital foram o Value at Risk e o Condicional Value at Risk. / [en] Financial regulatory agencies have been encouraging the adoption, in risk management practices, of internal models in order to determinate the regulatory minimum capital. Most of the models can be decomposed in minor capital models, each associated to a particular risk source to which that the company is exposed. The regulatory capital will be the aggregation of these individual capitals. The companies´ risks may have non-linear dependencies which prevent the sum of the individual capitals. One of the greatest challenges of this modeling process is to identify, measure and incorporate the dependencies amongst the several risk sources. The relatively recent copula theory has been shown to offer an effective tool for the aggregation of capitals, by duly capturing and incorporating the dependence of the several risks sources when estimating the minimum capital. This dissertation presents a general discussion about a dependence measurement methodology between risks. This is then applied, at the end of dissertation, to the estimation of the economic capital of an insurance company. Since copulas allow us to separate the effects of the structure dependence to the peculiar characteristics of the marginal distribution, it is possible to explore the impact of dependencies of risks on the total economic capital. The sensitivities of the economic capital are investigated. The risks measures used to determinate the capital were the Value at Risk and Conditional Value at Risk.

金融市場的激烈震盪，往往會造成投資大眾與企業的重大損失，甚而危及企業的生存及整體金融市場的穩定與發展。而每當金融市場發生變化時首當其衝者常為金融證券相關產業。證券商所面臨之經營風險雖可區分為市場風險、信用風險、流動性風險、作業風險、法律風險及系統風險等六類，但以市場風險為最主要的風險來源，由近年來國內外多起金融機構的重大損失案例可為證。大型化，國際化及多元化為國內證券商之發展趨勢，由於業務多元化、大型化，將使證券商所持有之金融資產部位增加，業務複雜度、組織運作與管理難度增加，相對的經營風險亦提高。因此適當的風險管理機制，以維持良好的風險管理能力，與適當的資源配置是證券商在致力於追求業務擴展之餘，應加以特別注意的重要事項。 本研究主要在探討國內證券商所面對的經營風險有那些，以及其在風險管理上存在的問題與建議，並對主要的市場風險管理問題尋求解決方案及進行個案分析。風險控管的內涵主要包括：風險管理的組織運作、風險衡量之技術、風險管理之策略、風險管理政策與執行等。除探討一般風險管理之策略運用(風險分散、風險移轉、風險承擔及動態避險等的原理與方法)外，並就近年來頗受注目的，風險值風險衡量管理技術的運用與模型進行研究，包括一般所定義之風險值的說明與實務運用外，進一步討論個別模型（包括歷史模擬法、蒙地卡羅模擬法、變異數-共變異數法及波動度之衡量方式等）的計算方法、特點。而在證券商之現行風險管理政策方面，則著重於證券商風險控管之外部規範與內部制度及其所存在的問題。 而就國內證券商所面對的風險管理問題與對策，本文以為除了必須要注重人才的培育召募及落實管理制度的執行外，還必須要有一具效率的風險管理工具及符合風險管理需要的組織與運作模式。就『有效率的風險管理工具』的問題，由於財務工程的原理與資訊科技的技術，可以幫助企業在市場環境快速變化下，迅速掌握企業在經營各項業務與投資決策時所面臨的風險大小與風險承擔能力進而採取適當的避險策略以規避風險。本文建議以建構『風險值風險管理資訊系統』以為解決對策，而就『符合風險管理需要的組織與運作模式』的問題，本文則建議以建構『專業分工、權力制衡、風控獨立、風險績效衡量』的組織運作模式為解決方案。

在台灣即將加入WTO的前提下，各家券商、銀行等金融業者為了提升本身的競爭力不斷追求利潤最大化以及風險最小化為其首要目標，因此風險控管的重要性便與日遽增，風險管理的方法也不斷推陳出新，在眾多的方法中，如何尋求最適自身的方法，便是各家金融業者刻不容緩研究的課題，風險值（Value at Risk）便是近期發展出來的一種風險控管工具。 　本研究以台灣債券組合為例，建構短期與長期公債的投資組合進行評估，研究方法採用一階、二階常態法、偏態修正法、蒙第卡羅模擬法及歷史資料模擬法，並配合不同的信賴水準、移動視窗及不同的利率期間結構及標準差估計法，對債券投資組合進行比較分析與驗証。在風險值驗證方面，則採用回溯測試與前向測試兩種驗證方法加上統計學上的平均值與變異數兩種方法，分別對上述不同的模型方法作驗證。