Neste trabalho, aprofundamos o estudo sobre risco sistêmico via funções de agregação. Consideramos três carteiras diferentes como proxy para um sistema econômico, estas carteiras são consistidas por duas funções de agregação, baseadas em todos as ações do E.U.A, e um índice de mercado. As medidas de risco aplicadas são Value at Risk (VaR), Expected Shortfall (ES) and Expectile Value at Risk (EVaR), elas são previstas através do modelo GARCH clássico unido com nove funções de distribuição de probabilidade diferentes e mais por um método não paramétrico. As previsões são avaliadas por funções de perda e backtests de violação. Os resultados indicam que nossa abordagem pode gerar uma função de agregação adequada para processar o risco de um sistema previamente selecionado. / In this work, we deepen the study of systemic risk measurement via aggregation functions. We consider three different portfolios as a proxy for an economic system, these portfolios are consisted in two aggregation functions, based on all U.S. stocks and a market index. The risk measures applied are Value at Risk (VaR), Expected Shortfall (ES) and Expectile Value at Risk (EVaR), they are forecasted via the classical GARCH model along with nine distribution probability functions and also by a nonparametric approach. The forecasts are evaluated by loss functions and violation backtests. Results indicate that our approach can generate an adequate aggregation function to process the risk of a system previously selected.

O objetivo principal deste artigo é estimar a contribuição dos bancos no mercado financeiro brasileiro ao risco sistêmico utilizando a metodologia proposta por Adrian e Brunnermeier (2011). Esta aplicação é relevante do ponto de vista de avaliação da regulação vigente, e na verificação dos padrões de risco vigentes mercado nacional. Entre os resultados encontrados, destacam-se três pontos distintos: (a) há uma grande divergência nos patamares de risco entre os períodos de baixa e alta estabilidade monetária; (b) a relação entre tamanho e risco gerado pelas instituições financeiras é não linear; e (c) assim como visto em trabalhos aplicados a outros países, o Value at Risk nem sempre acompanha a contribuição de um banco ao risco sistêmico, colocando em xeque as métricas da regulação vigente. / The main goal this of this paper is estimate the systemic risk contribution of the banks in the Brazilian financial markets, using the CoVaR methodology proposal in Adrian and Brunnermeier (2011). This application is relevant from the point of view of the effective regulation, and the examination of the patterns of the national market risk. Among the obtained results, stand out are three distinctive points: (a) there is a huge difference in levels of risk between poor and high stability environments; (b) the relationship between size and risk generated by financial institutions is not linear; and (c) as seen in previous works applied in others countries, the Value at Risk does not always follow the bank risk contribution to systemic risk, jeopardizing the metrics of the effective regulation.

Quantifier et mesurer le risque dans un environnement partiellement ou totalement incertain est probablement l'un des enjeux majeurs de la recherche appliquée en mathématiques financières. Cela concerne l'économie, la finance, mais d'autres domaines comme la santé via les assurances par exemple. L'une des difficultés fondamentales de ce processus de gestion des risques est de modéliser les actifs sous-jacents, puis d'approcher le risque à partir des observations ou des simulations. Comme dans ce domaine, l'aléa ou l'incertitude joue un rôle fondamental dans l'évolution des actifs, le recours aux processus stochastiques et aux méthodes statistiques devient crucial. Dans la pratique l'approche paramétrique est largement utilisée. Elle consiste à choisir le modèle dans une famille paramétrique, de quantifier le risque en fonction des paramètres, et d'estimer le risque en remplaçant les paramètres par leurs estimations. Cette approche présente un risque majeur, celui de mal spécifier le modèle, et donc de sous-estimer ou sur-estimer le risque. Partant de ce constat et dans une perspective de minimiser le risque de modèle, nous avons choisi d'aborder la question de la quantification du risque avec une approche non-paramétrique qui s'applique à des modèles aussi généraux que possible. Nous nous sommes concentrés sur deux mesures de risque largement utilisées dans la pratique et qui sont parfois imposées par les réglementations nationales ou internationales. Il s'agit de la Value at Risk (VaR) qui quantifie le niveau de perte maximum avec un niveau de confiance élevé (95% ou 99%). La seconde mesure est l'Expected Shortfall (ES) qui nous renseigne sur la perte moyenne au delà de la VaR.

Este trabalho apresenta um estudo através da abordagem Bayesiana em modelos de volatilidade estocástica, para modelagem de séries temporais financeiras, com o uso do método de Monte Carlo Hamiltoniano (HMC). Propomos o uso de outras distribuições para os erros da equação de observações do modelos de volatilidade estocástica, além da distribuição Gaussiana, para tratar problemas como caudas pesadas e assimetria nos retornos. Além disso, utilizamos critérios de informações, recentemente desenvolvidos, WAIC e LOO que aproximam a metodologia de validação cruzada, para realizar a seleção de modelos. No decorrer do trabalho, estudamos a qualidade do método HMC através de exemplos, estudo de simulação e aplicação a conjunto de dados. Adicionalmente, avaliamos a performance dos modelos e métodos propostos através do cálculo de estimativas para o Valor em Risco (VaR) para múltiplos horizontes de tempo. / This paper presents a study using Bayesian approach in stochastic volatility models for modeling financial time series, using Hamiltonian Monte Carlo methods (HMC). We propose the use of other distributions for the errors of the equation at stochastic volatiliy model, besides the Gaussian distribution, to treat the problem as heavy tails and asymmetry in the returns. Moreover, we use recently developed information criteria WAIC and LOO that approximate the crossvalidation methodology, to perform the selection of models. Throughout this work, we study the quality of the HMC methods through examples, simulation study and application to dataset. In addition, we evaluated the performance of the proposed models and methods by calculating estimates for Value at Risk (VaR) for multiple time horizons.

確保保險公司之清償能力是保險監理單位之首要目標，監理單位使用各種不同的監理制度以確保保險公司的財務體質，並防止保單持有人因為保險公司失去清償能力所遭致之損失。在各種監理制度中，RBC監理制度主要是衡量保險公司的資本適足性並且提供監理單位採取相關監理行動的準則；VaR監理制度則是目前銀行業之監理所嘗試採取的新監理方式，而且VaR也被廣泛運用在銀行內部的風險管理系統中，由銀行監理的發展趨勢看來，可以預期保險監理將來也會以VaR監理制度為主。 本研究的主要目的在於探討VaR監理制度適用在保險監理制度上的可行性以及與現行RBC監理制度的比較。在探討VaR監理制度的可行性前，本研究先就VaR監理制度運用在保險監理的前提以及影響保險公司失去清償能力的原因進行探討。 在瞭解影響保險公司失去清償能力的原因後，本研究分別對於在VaR監理制度下保險公司如何分別針對各種不同的風險因子決定所需持有的資本額度。經過相關文獻的探討以及考慮保險業的行業特性，本研究建議市場風險與核保風險可以用VaR計算其資本額度；信用風險由於尚未有十分完善的量化模型，所以本研究建議應以徵信方式因應此一風險，而業務風險則是以規定一固定比率的資本額度因應之。本研究也建議待保險公司累積足夠的VaR使用經驗後，保險監理制度可以開放使用預先承諾法。 在運用VaR於保險監理上時，本研究也建議監理單位必須注意有關VaR的實行風險與模型風險的影響，同時也強調監理單位的檢核與市場制度的力量是VaR監理制度能夠充分運作的必要條件；此外，由於制度實施的初期，無法驗證模型與資料的可用性，所以仍必須輔以最低固定比率的要求，以確保保險公司的清償能力。 在探討VaR運用在保險監理制度上的可行性後，本研究將進一步比較VaR與現行RBC監理制度的比較。本研究主要是由制度實行的難易程度、衡量資本適足的準確性，以及監理的成本三方面進行比較。制度實行的難易程度主要是比較VaR與RBC制度的複雜度與可行性，以及與公司內部風險管理和全球金融監理趨勢的整合程度。衡量資本適足的準確性主要是比較二種制度何者更可以衡量保險公司所面臨的各種風險、清償能力的效力，以及保險公司投資組合的風險分散效果。至於監理的成本則可分為監理者、保險公司與社會成本三方面來探討。 透過本研究的比較結果發現VaR監理制度除了在制度的複雜度與可行性較RBC制度差以外，其他項目皆優於RBC監理制度。除此之外，VaR與RBC都各自有其監理上的道德風險。本研究建議如同銀行監理一般，保險監理制度應朝向VaR監理制度的趨勢前進，以更可以確保保險公司的清償能力以及投保大眾的權益。 / Assuring insurance company solvency has always been the focal point of insurance regulation. Regulators use various methods to promote insurers' financial strength and protect policyholders from losses due to insolvency. Among these methods, risk-based capital (RBC) is used to measure the insurer's capital adequacy and provide the relative action rule for the regulator, and the VaR (value-at-risk) regulation is new regulatory type the bank regulator attempt to adopt. Besides the regulatory application, VaR is also used in bank's risk management system broadly. We can expect the VaR-type regulation will be the new insurance regulation in the future according to the development of bank's regulation. The methodology of this study adopt is literature review. The most important purpose of this study is to explore the feasibility of VaR-type insurance regulation and compare the VaR regulation with current RBC regulation. Before the regulation system examination, this study firstly discusses the presupposition of the VaR regulation application and the causes of insurer insolvency. For the purpose of developing the VaR-type capital requirement in insurance regulation, this study proposes that market and underwriting risk capital requirement can be directly calculated in VaR; credit and business risk capital requirement should be regulated a fixed-rate capital amount. This study also proposes the application of precommitment approach when the regulator assure the insurer accumulate good experience in VaR. In addition, this study also addresses some points for attention of VaR insurance regulation. The other purpose of this study is to compare the RBC and VaR through the regulatory implementation, solvency measurement, and regulatory cost. The result of this study indicates that VaR is superior to RBC in any aspect, besides the complexity and feasibility. In addition, VaR and RBC both have their own regulatory moral hazard. This study suggests VaR should be used in the insurance regulation as other financial regulation in the future.

Η πολύπλοκη μορφή που απέκτησαν οι χρηματοοικονομικές αγορές κατά τη διάρκεια των δύο τελευταίων δεκαετιών, είχε ως αποτέλεσμα την απώλεια πολύ υψηλών κεφαλαίων από τις επιχειρήσεις και από τις τράπεζες. Η ανάγκη για συστηματική μέτρηση του χρηματοοικονομικού κινδύνου οδήγησε στην επινόηση του μεγέθους της αξίας σε κίνδυνο (Value-at-Risk, VaR). Η μέθοδος αυτή παρέχει στον ενδιαφερόμενο έναν αριθμό που εκφράζει τη μέγιστη αναμενόμενη ζημία μίας επένδυσης για δεδομένη χρονική περίοδο και δεδομένο επίπεδο εμπιστοσύνης. Παρά το γεγονός ότι η VaR έχει κάποιους περιορισμούς που απαιτούν τη χρήση stress test και scenario test, συνολικά, η VaR είναι η καλύτερη ανεξάρτητη τεχνική μέτρησης των κινδύνων που είναι διαθέσιμη. Στόχος της παρούσας διπλωματικής εργασίας είναι η μέτρηση της VaR ενός χαρτοφυλακίου. Επιπλέον, μέσα από αυτήν την εργασία θα γίνει κατανοητό τι είναι η VaR, πώς μπορεί να υπολογιστεί, ποια είναι τα κύρια χαρακτηριστικά της και ποια είναι τα πλεονεκτήματα και τα μειονεκτήματά της. Τέλος, ιδιαίτερη έμφαση δίνεται στην παρουσίαση των μεθόδων υπολογισμού της VaR. / The inextricable form of the financial markets during the last two decades result in the loss of high capital from the businesses and banks. The need of a systemic measurement of the financial risk leads to the invention of the Value-at-Risk method. This method provides the interested person with a number which expresses the potential maximum loss of an investment for a given period of time and a given confidence level. Despite the fact that VaR has some restrictions demanding the use of stress test and scenario test, altogether, VaR is the best independent measuring technique of the risks that it is available. The aim of this dissertation is to measure the VaR of a portfolio. Moreover, it will be registered what VaR is, how it can be measured, which are its main characteristics, its advantages and disadvantages. Lastly, more emphasis is given to the presentation of the measuring methods of VaR.

Submitted by Luciano Rachman (lucianora@uol.com.br) on 2013-09-03T14:15:04Z No. of bitstreams: 1 Dissertacao_Luciano_Rachman.pdf: 1167975 bytes, checksum: da1c59096eda72630b44358c1d1e0b0f (MD5) / Approved for entry into archive by Suzinei Teles Garcia Garcia (suzinei.garcia@fgv.br) on 2013-09-03T14:52:47Z (GMT) No. of bitstreams: 1 Dissertacao_Luciano_Rachman.pdf: 1167975 bytes, checksum: da1c59096eda72630b44358c1d1e0b0f (MD5) / Made available in DSpace on 2013-09-03T15:05:37Z (GMT). No. of bitstreams: 1 Dissertacao_Luciano_Rachman.pdf: 1167975 bytes, checksum: da1c59096eda72630b44358c1d1e0b0f (MD5) Previous issue date: 2013-08-07 / As perdas trabalhistas nas Instituições Financeiras representam um valor considerável que devem ser consideradas no modelo de capital regulatório para risco operacional, segundo Basileia. A presente dissertação demonstra uma forma de mensurar o risco às quais as Instituições Financeiras estão expostas nesse tipo de perdas. Diversos tipos de distribuições são analisados conforme sua aderência tanto na frequência como na severidade das perdas. Para os valores de frequência, foi obtida uma amostra de dados real, enquanto para a severidade foram utilizados valores obtidos de relatórios de instituto de pesquisa que serviram de insumo para os cálculos de ações trabalhistas conforme legislação brasileira vigente na CLT (Consolidação das Leis do Trabalho). / According to Basel, the labor losses in Financial Institutions represent a substantial value that should be regarded in the model of regulatory capital for operational risk. This dissertation demonstrates a way to measure the risk to which Financial Institutions are exposed to in this type of loss. Several types of distributions are analyzed according to their adherence both in frequency and severity of losses. For frequency values, it was obtained a sample of actual data, whilst for the severity were used values given from reports of research institute which served as an input for the calculations of labor actions according to the present Brazilian legislation in CLT (Consolidation of Labor Laws).

Quantifier et mesurer le risque dans un environnement partiellement ou totalement incertain est probablement l'un des enjeux majeurs de la recherche appliquée en mathématiques financières. Cela concerne l'économie, la finance, mais d'autres domaines comme la santé via les assurances par exemple. L'une des difficultés fondamentales de ce processus de gestion des risques est de modéliser les actifs sous-jacents, puis d'approcher le risque à partir des observations ou des simulations. Comme dans ce domaine, l'aléa ou l'incertitude joue un rôle fondamental dans l'évolution des actifs, le recours aux processus stochastiques et aux méthodes statistiques devient crucial. Dans la pratique l'approche paramétrique est largement utilisée. Elle consiste à choisir le modèle dans une famille paramétrique, de quantifier le risque en fonction des paramètres, et d'estimer le risque en remplaçant les paramètres par leurs estimations. Cette approche présente un risque majeur, celui de mal spécifier le modèle, et donc de sous-estimer ou sur-estimer le risque. Partant de ce constat et dans une perspective de minimiser le risque de modèle, nous avons choisi d'aborder la question de la quantification du risque avec une approche non-paramétrique qui s'applique à des modèles aussi généraux que possible. Nous nous sommes concentrés sur deux mesures de risque largement utilisées dans la pratique et qui sont parfois imposées par les réglementations nationales ou internationales. Il s'agit de la Value at Risk (VaR) qui quantifie le niveau de perte maximum avec un niveau de confiance élevé (95% ou 99%). La seconde mesure est l'Expected Shortfall (ES) qui nous renseigne sur la perte moyenne au delà de la VaR. / To quantify and measure the risk in an environment partially or completely uncertain is probably one of the major issues of the applied research in financial mathematics. That relates to the economy, finance, but many other fields like health via the insurances for example. One of the fundamental difficulties of this process of management of risks is to model the under lying credits, then approach the risk from observations or simulations. As in this field, the risk or uncertainty plays a fundamental role in the evolution of the credits; the recourse to the stochastic processes and with the statistical methods becomes crucial. In practice the parametric approach is largely used.It consists in choosing the model in a parametric family, to quantify the risk according to the parameters, and to estimate its risk by replacing the parameters by their estimates. This approach presents a main risk, that badly to specify the model, and thus to underestimate or over-estimate the risk. Based within and with a view to minimizing the risk model, we choose to tackle the question of the quantification of the risk with a nonparametric approach which applies to models as general as possible. We concentrate to two measures of risk largely used in practice and which are sometimes imposed by the national or international regulations. They are the Value at Risk (VaR) which quantifies the maximum level of loss with a high degree of confidence (95% or 99%). The second measure is the Expected Shortfall (ES) which informs about the average loss beyond the VaR.

[pt] Um dos principais desafios no mercado financeiro é simular preços mantendo a estrutura de correlação entre os inúmeros ativos de um portfólio. Análise de Componentes Principais emerge como uma solução para este último problema. Além disso, dada a incerteza presente nos mercados de commodities de derivados de petróleo, o investidor quer proteger seus ativos de perdas potenciais. Como uma alternativa a esse problema, a otimização de várias medidas de risco, como Value-at-risk, Conditional Value-at-risk e medida Ômega, são ferramentas financeiras importantes. Além disso, o backtest é amplamente utilizado para validar e analisar o desempenho do método proposto. Nesta dissertação, trabalharemos com um portfólio de commodities de petróleo. Vamos unir diferentes técnicas e propor uma nova metodologia que consiste na diminuição da dimensão do portfólio proposto. O passo seguinte é simular os preços dos ativos na carteira e, em seguida, otimizar a alocação do portfólio de commodities de derivados do petróleo. Finalmente, vamos usar técnicas de backtest, a fim de validar nosso método. / [en] One of the main challenges in the financial market is to simulate prices keeping the correlation structure among numerous assets. Principal Component Analysis emerges as solution to the latter problem. Also, given the uncertainty present in commodities markets, an investor wants to protect his/her assets from potential losses, so as an alternative, the optimization of various risk measures, such as Value-at-risk, Conditional Value-at-risk and Omega Ratio, are important financial tools. Additionally, the backtest is widely used to validate and analyze the performance of the proposed methodology. In this dissertation, we will work with a portfolio of oil commodities. We will put together different techniques and propose a new methodology that consists in the (potentially) decrease the dimension of the proposed portfolio. The following step is to simulate the prices of the assets in the portfolio and then optimize the allocation of the portfolio of oil commodities. Finally, we will use backtest techniques in order to validate our method.

本文提出了一個新興風險衡量的工具的概念-期望尾端損失值(ETL)，其有別於風險值為百分位數且未考慮報酬分配的尾部風險(Tail Risk)，本研究期望能透過ETL的估計可以更完整表達投資組合所有可能面臨的風險，對於市場風險能更有效控管。 本文實證討論有關VaR與ETL穩定度的部分，VaR雖然在理論上證明無法滿足次可加性這個條件，但是在本研究實證中，即使在分配具厚尾狀況下，VaR仍滿足次加性的性質。這也表示，我們在現實生活中很難因VaR理論上缺乏次可加性，而捨棄VaR這個風險衡量工具，然ETL也有其貢獻性，其較VaR多考慮尾部資訊，可視為風險值外另一參考指標，此為本文貢獻一。 本文實證也探討移動窗口中歷史資料長度的不同，是否造成VaR與ETL估算準確性的差異，本文由實證結果發現：在歷史窗口的資料長度越長(1000日)下，並沒有正確預估VaR與ETL，而本研究中以移動窗口為500日下，使用內部模型較具正確性，故在使用風險值模型時，應謹慎選擇移動窗口之長度，此為本文貢獻二。