【第一篇論文中文摘要】 集中度風險於結構式商品的量化與分析：以房屋抵押貸款證券為例 "Martin and Wilde (2002)與Gordy (2003)" 針對巴塞爾協定(Basel Accords)中金融機構之投資組合所內藴之集中度風險提出了相對應的微粒化調整(Granularity Adjustment)風險量化準則，然而該模型僅止於單因子架構下探究單一信用標的集中度風險之量化。本文將其架構延用至結構式商品中，允許債權群組內之信用標的具不同區域別，我們採用Hull and White(2010)之跨池違約相關性描述，並結合Pykhtin (2004)中延拓單因子聯繫模型至多因子之方式，進而求取債權群組之單一資產集中度(Name Concentration)與區域類別集中度(Sector Concentration)風險的量化。本文以房屋抵押貸款證券(Mortgage Backed Securities, MBSs)為例，於集中度風險的考量下，藉由檢視不同風險情境下分券之損失起賠點，重新評估房屋抵押貸款證券AAA投資級分券信用評級之合理性。研究結果顯示，AAA評等之分券高度曝險於系統性風險，且於高風險情境下，標的房貸之區域集中現象擴大了違約相關性對債權群組損失分配的影響，致使AAA分券之損失起賠點得以超過其實際擔保額度(subordination)範圍。 【第二篇論文中文摘要】 美國銀行放款多角化對其報酬與風險之影響：相關性與傳染的觀點 本文目的在於分析銀行放款的多角化行為對其報酬與風險之影響。研究發現納入銀行放款投資組合相關性之考量，亦即標的資產之相關性結構以及資產間因契約關係所隱含跨投資組合之傳染途徑，將降低多角化之成效。文中透過因子模型(factor model)建構資產之報酬，同時決定其相關性結構，其中將資產間殘差項相關性作為傳染指標，進一步分析投資組合內標的資產間的平均相關係數、傳染與多角化程度間的關聯性。我們以美國銀行作為研究樣本，分別以赫芬達-赫希曼指數估算投資組合權重分配之集中度、使用組合內標的產業股票報酬資訊來計算投資組合內相關程度，接著利用標的產業與投資組合外產業間的殘差相關性來捕捉產業傳染效果，將此三項指標作為衡量多角化指標，分析其在1987年至2014年間聯貸投資組合多角化情形並試圖分析放款多角化對銀行績效之影響。透過契約關係的界定進而探討顧客傳染如何影響銀行績效。 研究發現於市場處於平穩期間(tranquil period)，所有多角化指標銀行放款均呈現放款多角化程度越高越有助於提高銀行的報酬並降低其風險。然而於危機期間(turmoil period)，銀行應將放款權重集中於部分產業、建構相關性較低之組合或選擇較低之傳染效果之產業作為放款的對象，用以提高銀行績效。隱含在危機期間銀行應該選擇適度之多角化策略，若僅以赫芬達-赫希曼指數作為多角化之衡量將顯示危機期間越集中越有助於銀行的表現，此舉將造成解釋上的偏誤。說明於投資組合多角化的衡量上，不該忽略由相關性結構所引發之集中度風險。 / 【Essay I】 Quantification and Analysis of Concentration Risk in Structured Products: the Case of Mortgage Backed Securities Granularity adjustments, introduced by Martin and While (2002) and Gordy (2003), allow one to quantify the concentration exposures of credit portfolios due to imperfect diversification. However, they focus solely on name concentrations under an Asymptotic Single Risk Factor (ASRF) framework. In this study, by adapting the multi-pool correlation structure of Hull and White (2010) under the multi-factor setting of Pykhtin (2004), we derive quantitative measures of name and sector concentration that facilitate subsequent analysis of the risk profiles embedded in Mortgage Backed Securities (MBSs). Under different stress scenarios, we examine the impacts of concentration exposures on the internal credit enhancements, in particular, the AAA tranche attachment points. We show that, under severe market conditions, the presence of sector concentrations in the underlying mortgage pools can further amplify the effects of default correlation on the portfolio loss distributions. As a direct consequence, the predetermined subordination level determined by the assignment of tranche attachment points can be exceeded. 【Essay II】 How Loan Portfolio Diversification Affects U.S. Banks’ Return and Risk: Correlation and Contagion Perspectives. In this paper we investigate how loan portfolio diversification affects the banks’ return and risk. We argue that, the dependence structure of bank loan portfolios, namely, the correlation structure among loan assets and the presence of contagion channels due to contractual relationships across the border of portfolio, contributes to the costs of diversification. Under the factor model framework, we derive a theoretical model to depict the asset returns and their dependence structure. Based on data of US bank loans collected from 1987-2014, our empirical study employs HHI, intra-portfolio correlation, and contagion as proxies for diversification to examine how loan portfolio diversification affects the banks’ profitability and riskiness. In addition, contractual relationships are identified and we investigate how customer contagion affects the bank’s performance. We find that all diversification measures exhibit a positive effect on the performance of U.S. banks during tranquil periods. However, for turmoil periods, banks with loan portfolios of more concentrated weight distributions, lower intra-portfolio correlation, or lower consumer contagion effects would have improved returns and reduced risk. In other words, during crisis, banks should choose an appropriate concentration strategy rather than focus on selected industries as determined solely by the HHI.

[pt] Importante questão que se coloca atualmente é a capacidade de medição do volume de capital necessário, às sociedades seguradoras, para fazer frente aos diversos tipos de risco que tais companhias suportam no exercício de suas atividades. Esse volume de capital necessário deve ser tal que permita à companhia suportar variabilidades no negócio. As motivações para o desenvolvimento de modelos matemáticos visando à determinação desta necessidade de capital são tanto a preocupação das próprias companhias com a sua gestão de risco, como também aspectos relacionados ao estabelecimento de requerimentos de capital exigidos pelo regulador de seguro às sociedades seguradoras para fazer frente aos riscos suportados. Entre tais riscos, encontra-se a categoria dos riscos de subscrição, relacionados diretamente à operação central de uma seguradora (design de produto, precificação, processo de aceitação, regulação de sinistros e provisionamento). Esta dissertação apresenta uma proposta de modelo para determinação do volume necessário de capital para fazer frente aos riscos de subscrição, na qual tal categoria de riscos é segregada nos riscos de provisão de sinistros (relativos aos sinistros ocorridos e, assim, relacionados às provisões de sinistros) e nos riscos de emissão/precificação (relativos aos sinistros à ocorrer num horizonte de tempo de 1 ano, considerando novos negócios). Em especial, o modelo proposto utiliza processos de simulação que levam em consideração a estrutura de dependência das variáveis envolvidas e linhas de negócio, fazendo uso do conceito de cópulas condicionais. / [en] Important question that arises today is the ability to measure the amount of capital necessary to insurance companies, to cope with various types of risk that these companies support in performing their activities. This volume of capital required must be such as to enable the company to bear variability in business. The motivations for the development of mathematical models aimed at the determination of those capital needs are both the concern of companies with their own risk management, as well as aspects related to establishing capital requirements required by the insurance regulator to insurance companies to face the risks borne. Among such risks, is the category of underwriting risks, directly related to the core operation of an insurance company (product design, pricing, underwriting process, loss settlement and provisioning). This dissertation proposes a model for determining the appropriate amount of capital to cope with the underwriting risks, where such risk category is segregated in reserving risks (relative to incurred events) and pricing risks (relative to events occurring in the time horizon of 1 year, considering new businesses). In particular, the proposed model uses simulation processes that take into account the dependence structure of the variables involved and lines of business, making use of the concept of conditional copulas.

Quantification of risks is one of the pillars of the contemporary insurance industry. Natural catastrophes and their modelling represents one of the most important areas of non-life insurance in the Czech Republic. One of the key inputs of catastrophe models is a spatial dependence structure in the portfolio of an insurance company. Copulas represents a more general view on dependence structures and broaden the classical approach, which is implicitly using the dependence structure of a multivariate normal distribution. The goal of this work, with respect to absence of comprehensive monographs in the Czech Republic, is to provide a theoretical basis for use of copulas. It focuses on general properties of copulas and specifics of two most commonly used families of copulas -- Archimedean and elliptical. The other goal is to quantify difference between the given copula and the classical approach, which uses dependency structure of a multivariate normal distribution, in modelled flood losses in the Czech Republic. Results are largely dependent on scale of losses in individual areas. If the areas have approximately a "tower" structure (i.e., one area significantly outweighs others), the effect of a change in the dependency structure compared to the classical approach is between 5-10% (up and down depending on a copula) at 99.5 percentile of original losses (a return period of once in 200 years). In case that all areas are approximately similarly distributed the difference, owing to the dependency structure, can be up to 30%, which means rather an important difference when buying the most common form of reinsurance -- an excess of loss treaty. The classical approach has an indisputable advantage in its simplicity with which data can be generated. In spite of having a simple form, it is not so simple to generate Archimedean copulas for a growing number of dimensions. For a higher number of dimensions the complexity of data generation greatly increases. For above mentioned reasons it is worth considering whether conditions of 2 similarly distributed variables and not too high dimensionality are fulfilled, before general forms of dependence are applied.

Cette thèse se propose d’analyser la structure et la dynamique de dépendance de crédit des institutions financières aux Etats-Unis et en Europe durant la crise financière de 2008. Un premier chapitre présente une revue de la littérature des modèles multi-dimensionnels de crédit et des modèles économétriques de contagion financière. Ce chapitre a pour vocation de guider notre réflexion à la fois conceptuelle et méthodologique sur les hypothèses analytiques de la contagion ainsi que ses méthodes de mesure. Nous montrons que si la contagion est devenue une hypothèse centrale des modèles multivariés de risque de crédit, il n’en reste néanmoins que sa définition et sa quantification ne font pas l’objet de consensus dans la littérature. Un deuxième chapitre propose une analyse empirique des co-movements des rendements de CDS de banques et sociétés d’assurance américaines et européennes. La dissociation de leur structure de dépendance entre association linéaire et dépendances extrêmes nous permet de mettre en évidence des phénomènes d'interconnexions entre institutions financières apparues au courant de la crise et véhiculant ainsi sous l'effet de la contagion, un risque systémique croissant. Un dernier chapitre présente une interprétation économique des résultats obtenus dans notre deuxième chapitre. En particulier, nous cherchons à quantifier l'influence jouée par la contagion et les facteurs de risques communs sur la dynamique de dépendance extrême des institutions financières. Nous démontrons ainsi le rôle du risque de contrepartie, du risque de liquidité et du risque de défaut des institutions financières dans la transmission de la contagion sur le marché de CDS. / This thesis examines the credit dependence structure and dynamics of financial institutions in the U.S. and Europe amid the recent financial crisis. A first chapter presents a survey of multi-name models of credit risk and econometric models of financial contagion with the purpose of guiding both the analytical and conceptual assumptions and econometric modelling techniques we use in the subsequent chapters. We show that if contagion has become a central cornerstone of multi-name models of credit risk, there is nonetheless a lack of consensus on the way to both define and measure it. A second chapter presents the results of an empirical analysis of U.S. and European banks and insurance companies’ CDS return extreme co-movements. By uncovering financial institutions' linear as well as extremal dependence structures, we provide evidence that their credit dependence has strengthened during the crisis, thereby effectively conveying, in the face of extreme tail events, potential systemic risks. A third and last chapter provides an economic rationale of the results presented in our second chapter. In particular, we examine the impact of common risk factors and contagion on the dynamics of financial institutions' extremal credit dependence. We demonstrate the role of counterparty risk and liquidity risk, as well the repricing by market participants since July 2007 of their jump-to-default premia as additional channels driving financial institutions' increased dependence and amplifying contagion on the CDS market.

Dans cette thèse, nous abordons l'estimation non paramétrique de la fonction de dépendance des distributions multivariées à valeurs extrêmes. Dans une première partie, on adopte l’hypothèse classique stipulant que les variables aléatoires sont indépendantes et identiquement distribuées (i.i.d). Plusieurs estimateurs non paramétriques sont comparés pour une fonction de dépendance trivariée de type logistique dans deux différents cas. Dans le premier cas, on suppose que les fonctions marginales sont des distributions généralisées à valeurs extrêmes. La distribution marginale est remplacée par la fonction de répartition empirique dans le deuxième cas. Les résultats des simulations Monte Carlo montrent que l'estimateur Gudendorf-Segers (Gudendorf et Segers, 2011) est plus efficient que les autres estimateurs pour différentes tailles de l’échantillon. Dans une deuxième partie, on ignore l’hypothèse i.i.d vue qu’elle n'est pas vérifiée dans l'analyse des séries temporelles. Dans le cadre univarié, on examine le comportement extrêmal d'un modèle autorégressif Gaussien stationnaire. Dans le cadre multivarié, on développe un nouveau théorème qui porte sur la convergence asymptotique de l'estimateur de Pickands vers la fonction de dépendance théorique. Ce fondement théorique est vérifié empiriquement dans les cas d’indépendance et de dépendance asymptotique. Dans la dernière partie de la thèse, l'estimateur Gudendorf-Segers est utilisé pour modéliser la structure de dépendance des concentrations extrêmes d’ozone observées dans les stations qui enregistrent des dépassements de la valeur guide et limite de la norme Tunisienne de la qualité d'air NT.106.04. / In this thesis, we investigate the nonparametric estimation of the dependence function for multivariate extreme value distributions. Firstly, we assume independent and identically distributed random variables (i.i.d). Several nonparametric estimators are compared for a trivariate dependence function of logistic type in two different cases. In a first analysis, we suppose that marginal functions are generalized extreme value distributions. In a second investigation, we substitute the marginal function by the empirical distribution function. Monte Carlo simulations show that the Gudendorf-Segers (Gudendorf and Segers, 2011) estimator outperforms the other estimators for different sample sizes. Secondly, we drop the i.i.d assumption as it’s not verified in time series analysis. Considering the univariate framework, we examine the extremal behavior of a stationary Gaussian autoregressive process. In the multivariate setting, we prove the asymptotic consistency of the Pickands dependence function estimator. This theoretical finding is confirmed by empirical investigations in the asymptotic independence case as well as the asymptotic dependence case. Finally, the Gudendorf-Segers estimator is used to model the dependence structure of extreme ozone concentrations in locations that record several exceedances for both guideline and limit values of the Tunisian air quality standard NT.106.04.