This thesis investigates correlations and linkages in credit risk that widely exist in all sectors of the financial markets. The main body of this thesis is constructed around four empirical chapters. I started with extending two main issues focused by earlier empirical studies on credit derivatives markets: the determinants of CDS spreads and the relationship between CDS spreads and bond yield spreads, with a special focus on the effect of the subprime crisis. By having observed that the linear relationship can not fully explain the variation in CDS spreads, the third empirical chapter investigated the dependence structure between CDS spread changes and market variables using a nonlinear copula method. The last chapter investigated the relationship between the CDS spread and another credit spread - the TED spread, in that a MVGARCH model and twelve copulas are set forth including three time varying copulas. The results of this thesis greatly enhanced our understanding about the effect of the subprime crisis on the credit default swap market, upon which a set of useful practical suggestions are made to policy makers and market participants.

本文主要藉由逐次改變二次擔保債權憑證的內層分券金額佔資產池發行金額比例、內層分券下層信用保護金額佔資產池金額比例、資產池參考標的間違約相關性、到期期限、及違約回收率等五項影響二次擔保債權憑證損失發生機率的風險因子，結合蒙地卡羅模擬法及關聯結構法模擬交易架構中內層、外層分券不同損失率的發生機率，並利用彈性分析，衡量二次擔保債券憑證在每單位風險因子變動下，內層及外層分券的損失發生機率。 研究結果顯示，相同的風險因子對於內層與外層分券的損失發生機率的影響效果並不相同，此一現象有別於一般認為風險因子對內、外層分券損失發生機率影響效果相同的看法。此外，依據分券損失發生機率對每單位風險因子變化的彈性敏感性分析，分券損失發生機率受風險因子的影響可分為: 彈性為正且數值逐漸增加、彈性為正且逐漸下降、彈性為負且數值 (絕對值) 逐漸下降、及彈性為負且數值 (絕對值) 逐漸增加四類。外層夾層分券的損失發生機率對內層分券厚度占資產池金額比例的彈性為負，其數值 (絕對值) 隨著內層分券厚度占資產池金額比例的增加而下降。外層夾層分券的損失發生機率對內層分券下層信用保護金額佔資產池金額比例的彈性、及外層夾層分券的損失發生機率對參考標的違約回收率的彈性為負，且數值 (絕對值) 隨著下層信用保護比例及回收率的增加而上升。外層夾層分券的損失發生機率對參考標的違約相關係數的彈性為正，其數值隨著相關係數的增加而下降；外層夾層分券的損失發生機率對參考標的之到期期限的彈性為正，其數值隨著到期期限的增加而上升。 / The researchers of this study combined Monte Carlo simulation approach and copula method to change the following five risk factors: the thickness of inner CDOs tranche on CDO-squared, the subordination in master CDOs tranche, the correlation of reference entities, the maturity of reference entities, and the recovery rate of reference entities, with a purpose of simulating the loss possibility of CDOs-squared. Besides, by elasticity analysis, the researchers measured the change of loss rate according to the change of each risk factor per unit. The result of the study shows that the same risk factor has different influence on the loss rate of inner and master tranche of CDOs squared, which mismatches the general belief that the same risk factor has the same effect on the loss rate of inner and master CDOs tranche. In addition, according to the tranche loss possibility elasticity analysis to the risk factors, this research reveals that four categories can be made due to the effect which risk factors have on loss rate : positive and increasing elasticity, positive and decreasing elasticity, negative and increasing elasticity, and negative decreasing elasticity. We found that for the master mezzanine tranche: the elasticity of tranche loss possibility to the thickness of inner CDOs tranche of CDO-squared is negative and will decrease with the increasing thickness of inner CDOs tranche. The elasticity of tranche loss possibility to subordination in inner CDOs tranche and the elasticity of tranche loss possibility to the recovery rate of reference entities are both negative and will increase with the increasing subordination of inner CDOs tranche and the recovery rate of reference entities. The elasticity of the loss rate possibilities to the correlation of reference entities default is positive and will decrease with the increasing correlation of reference entities. The elasticity of loss possibilities to the maturity of reference entities is positive and will increase with the increasing maturity.

相較於單一信用違約交換只能對單一信用標的進行信用保護，一籃子信用違約交換則能對一籃子的信用標的進行信用保護。此種產品的評價決定於一籃子信用標的實體的聯合機率分配，因此多個標的資產間違約相關性的衡量，對於一籃子信用違約交換的評價和風險管理是相當重要的課題。 　　在一個資產池中，有時可以將其切割成兩個以上的群體，各群體間彼此相互獨立，而在各群內彼此相依。我們將其視為在多因子模型下的特例，此模型提供我們更具彈性的方式去建立資產之間彼此的相關性。 　　在這篇文章中，我們主要以 Chiang, Yueh, and Hsieh (2007) 在單因子模型下所提出來的方法為基礎，將其延伸至多因子的模型下的特例。藉由選擇一個合適的(IS)分配，在每一次的模擬中必定會有k個違約事件發生；因此我們獲得一個有效率的方法對一籃子違約交換進行評價，此演算法不僅簡單並且其變異數較蒙地卡羅小。 / In contrast to a single name credit default swaps which provides credit protection for a single underlying, a basket credit default swap extends the credit protection to portfolio of obligors with the restriction that the default of only one underlying is compensated. The price of the products depends on the joint default probability of the underlying in the credit portfolio. Thus, the modeling of default correlation, default risk and expected loss is a key issue for the valuation and risk management of basket default swaps. Sometimes a pool of underlying obligors can have two or more separate groups, between those they are unrelated, but in each part they are related. The special cases provide more flexible way to construct the correlation between two or more underlying obligors. In this paper, our approach is based on the construction of importance sampling (IS) method proposed by Chiang, Yueh and Hsieh (2007) under one-factor model, and then we extend the model to a special case under the multi-factor model. By the appropriate choice of the importance sampling distribution, we establish a way of ensuring that for every path generated, k default events always take place. Then we can obtain an efficiency algorithm for basket default swap valuation. The algorithm is simple to implement and it also guarantees variance reduction.

This thesis presents a class of graphical models for directly representing the joint cumulative distribution function (CDF) of many random variables, called cumulative distribution networks (CDNs). Unlike graphical models for probability density and mass functions, in a CDN, the marginal probabilities for any subset of variables are obtained by computing limits of functions in the model. We will show that the conditional independence properties in a CDN are distinct from the conditional independence properties of directed, undirected and factor graph models, but include the conditional independence properties of bidirected graphical models. As a result, CDNs are a parameterization for bidirected models that allows us to represent complex statistical dependence relationships between observable variables. We will provide a method for constructing a factor graph model with additional latent variables for which graph separation of variables in the corresponding CDN implies conditional independence of the separated variables in both the CDN and in the factor graph with the latent variables marginalized out. This will then allow us to construct multivariate extreme value distributions for which both a CDN and a corresponding factor graph representation exist. In order to perform inference in such graphs, we describe the `derivative-sum-product' (DSP) message-passing algorithm where messages correspond to derivatives of the joint cumulative distribution function. We will then apply CDNs to the problem of learning to rank, or estimating parametric models for ranking, where CDNs provide a natural means with which to model multivariate probabilities over ordinal variables such as pairwise preferences. We will show that many previous probability models for rank data, such as the Bradley-Terry and Plackett-Luce models, can be viewed as particular types of CDN. Applications of CDNs will be described for the problems of ranking players in multiplayer team-based games, document retrieval and discovering regulatory sequences in computational biology using the above methods for inference and estimation of CDNs.

In this paper dependence between credit default swap (CDS) values and stock price movements of the largest European banking groups is examined and effectiveness of the usage of CDS contracts as a tool to hedge exposure to the price movements of the underlying stock during the pre-crisis and crisis periods is assessed. The effectiveness is evaluated by comparing estimated Value-at-Risk (VaR) and Expected Shortfall (ES) risk measures of portfolios consisting of stocks and CDS vis-à-vis portfolios consisting of only stocks. CDS are valued using mark-to-market approach. Marginal distributions of CDS value changes and stock returns are estimated using Kernel density estimate from historical time-series data of daily stock returns and CDS value changes. Dependence between marginal distributions is estimated using Gaussian, Gumbel and Student‟s t copulas. Random portfolio values are simulated using Monte Carlo Simulation from estimated copulas parameters and marginal distributions for daily, quarterly and yearly time horizons. VaR and ES with 90%, 95% and 99% confidence level are estimated from the simulated portfolio return distribution. The results show that there is a significant negative dependence between CDS values and stock prices during financial crisis while dependence is weak in the pre-crisis period. The main finding of the paper is that CDS added into the portfolio of stocks significantly reduces VaR and ES of a portfolio during the period of financial crisis while they... [to full text] / Šiame darbe tikrinama didţiausių Europos bankų grupių kredito rizikos apsikeitimo sandorių (CDS) ir akcijų kainų priklausomybė bei vertinamas CDS efektyvumas, jei jais draudţiamasi nuo akcijų kainų svyravimų prieš kriziniu ir kriziniu laikotarpiu. Efektyvumas yra įvertinamas lyginant apskaičiuotas rizikos vertes (VaR) ir tikėtinus vertės trūkumus (ES) dviejų portfelių: akcijų portfelio bei akcijų ir CDS portfelio. CDS vertinti yra naudojamas pagal rinką vertinimo būdas (mark-to-market approach). CDS verčių pasikeitimo ir akcijų grąţos ribiniai pasiskirstymai yra įvertinami, naudojant Kernel įvertinimą (Kernel Estimator) iš istorinių akcijų grąţų ir CDS verčių pokyčių duomenų. Priklausomybė tarp ribinių pasiskirstymų yra įvertinama naudojant Gauso, Gumbelio ir Studento t kopulas (copulas). Atsitiktinės portfelių vertės yra susimuliuojamos naudojant Monte Carlo simuliaciją, pritaikant kopulų parametrus bei kintamųjų ribinius pasiskirstymus vienos dienos, ketvirčio bei metų periodams. VaR ir ES su 90%, 95% ir 99% pasitikėjimo intervalais yra skaičiuojami iš susimuliuotų portfelio grąţų pasiskirstymo. Gauti rezultatai rodo, kad tarp akcijų kainų ir CDS verčių yra stipri priklausomybė krizės laikotarpiu, tuo tarpu prieš kriziniu laikotarpiu priklausomybė yra silpna. Pagrindinė darbo išvada yra ta, jog CDS įtraukti į akcijų portfelį reikšmingai sumaţina portfelio VaR ir ES kriziniu laikotarpiu, tačiau nesumaţina prieš kriziniu laikotarpiu. Portfelio rizika gali būti sumaţinta, jei... [toliau žr. visą tekstą]

Cerebral autoregulation describes the clinically observed phenomenon that cerebral blood flow remains relatively constant in healthy human subjects despite large systemic changes in blood pressure, dissolved blood gas concentrations, heart rate and other systemic variables. Cerebral autoregulation is known to be impaired post ischaemic stroke, after severe head injury, in patients suffering from autonomic dysfunction and under the action of various drugs. Cerebral auto-regulation is a dynamic, multivariate phenomenon. Sensitive techniques are required to monitor cerebral auto-regulation in a clinical setting. This thesis presents 4 related signal processing studies of cerebral autoregulation. The first study shows how consideration of changes in blood gas concentrations simultaneously with changes in blood pressure can improve the accuracy of an existing frequency domain technique for monitoring cerebral autoregulation from spontaneous fluctuations in blood pressure and a transcranial doppler measure of cerebral blood flow velocity. The second study shows how the continuous wavelet transform can be used to investigate coupling between blood pressure and near infrared spectroscopy measures of cerebral haemodynamics in patients with autonomic failure. This introduces time information into the frequency based assessment, however neglects the contribution of blood gas concentrations. The third study shows how this limitation can be resolved by introducing a new time-varying multivariate system identification algorithm based around the dual tree undecimated wavelet transform. All frequency and time-frequency domain methods of monitoring cerebral autoregulation assume linear coupling between the variables under consideration. The fourth study therefore considers nonlinear techniques of monitoring cerebral autoregulation, and illustrates some of the difficulties inherent in this form of analysis. The general approach taken in this thesis is to formulate a simple system model; usually in the form of an ODE or a stochastic process. The form of the model is adapted to encapsulate a hypothesis about features of cerebral autoregulation, particularly those features that may be difficult to recover using existing methods of analysis. The performance of the proposed method of analysis is then evaluated under these conditions. After this testing, the techniques are then applied to data provided by the Laboratory of Human Cerebrovascular Physiology in Alberta, Canada, and the National Hospital for Neurology and Neurosurgery in London, UK.

<p>Teza istražuje mogućnost kori&scaron;ćenja kopule u finoj analizi međusobne zavisnosti kardiovaskularnih signala. U tu svrhu kori&scaron;ćene su različite GoF (Goodness of Fit) tehnike i matematički alati bazirani na kopuli. Predložena metoda određuje nivo zavisnosti kao funkciju vremenskog ka&scaron;njenja signala pulsnog intervala u odnosu na signal sistoličkog krvnog pritiska i omogućuje uvid u mehanizme otkucaj-po-otkucaj regulacije krvnog pritiska. Farmakolo&scaron;ka validacija je izvedena administracijom lekova koji inhibiraju autonomni nervni sistem, pri čemu su dobijeni rezultati imali jasan fiziolo&scaron;ki odziv.</p> / <p>The thesis investigates a possibility to apply a copula method for a more refined analysis of mutual dependency of cardiovascular signals. Different GoF (Goodness of Fit) techniques and mathematical tools based on copula are applied to prove this possibility. Proposed method determines the level of dependency of the pulse interval response in respect to the systolic blood pressure for different time lags and provides further insight into the beat-to-beat regulation of blood pressure. Pharmacological validation of the method was performed by administration of autonomic blockers drugs, as the obtained copula response was in accordance with the physiological interpretation.</p>

Ocean wave energy is considered to be one of the important potential renewable energy resources for sustainable development. Various wave energy converter technologies have been proposed to harvest the energy from ocean waves. This thesis is based on the linear generator wave energy converter developed at Uppsala University. The research in this thesis focuses on the foundation optimization and the power absorption optimization of the wave energy converters and on the wave climate modelling at the Lysekil wave converter test site. The foundation optimization study of the gravity-based foundation of the linear wave energy converter is based on statistical analysis of wave climate data measured at the Lysekil test site. The 25 years return extreme significant wave height and its associated mean zero-crossing period are chosen as the maximum wave for the maximum heave and surge forces evaluation. The power absorption optimization study on the linear generator wave energy converter is based on the wave climate at the Lysekil test site. A frequency-domain simplified numerical model is used with the power take-off damping coefficient chosen as the control parameter for optimizing the power absorption. The results show a large improvement with an optimized power take-off damping coefficient adjusted to the characteristics of the wave climate at the test site. The wave climate modelling studies are based on the wave climate data measured at the Lysekil test site. A new mixed distribution method is proposed for modelling the significant wave height. This method gives impressive goodness of fit with the measured wave data. A copula method is applied to the bivariate joint distribution of the significant wave height and the wave period. The results show an excellent goodness of fit for the Gumbel model. The general applicability of the proposed mixed-distribution method and the copula method are illustrated with wave climate data from four other sites. The results confirm the good performance of the mixed-distribution and the Gumbel copula model for the modelling of significant wave height and bivariate wave climate.

Cette thèse est une contribution à la modélisation imbriquée de systèmes complexes. Elle propose une méthodologie globale pour quantifier les incertitudes et leurs origines dans une chaîne de calcul formée par plusieurs modèles pouvant être reliés les uns aux autres de façon complexe. Ce travail est organisé selon trois axes. D’abord, la structure dedépendance des paramètres du modèle, induite par la modélisation imbriquée, est modélisée de façon rigoureuse grâce à la théorie des copules. Puis, deux méthodes d’analyse de sensibilité adaptées aux modèles à paramètres d’entrée corrélés sont présentées : l’une est basée sur l’analyse de la distribution de la réponse du modèle, l’autre sur la décomposition de la covariance. Enfin, un cadre de travail inspiré de la théorie des graphes est proposé pour la description de l’imbrication des modèles. La méthodologie proposée est appliquée à des exemples industriels d’envergure : un modèle multiéchelles de calcul des propriétés mécaniques du béton par une méthode d’homogénéisation et un modèle multiphysique de calcul de dommage sur la culasse d’un moteur diesel. Les résultats obtenus fournissent des indications importantes pour une amélioration significative de la performance d’une structure. / This thesis is a contribution to the nested modelling of complex systems. A global methodology to quantify uncertainties and their origins in a workflow composed of several models that can be intricately linked is proposed. This work is organized along three axes. First, the dependence structure of the model parameters induced by the nested modelling is rigorously described thanks to the copula theory. Then, two sensitivity analysis methods for models with correlated inputs are presented : one is based on the analysis of the model response distribution and the other one is based on the decomposition of the covariance. Finally, a framework inspired by the graph theory is proposed for the description of the imbrication of the models. The proposed methodology is applied to different industrial applications : a multiscale modelling of the mechanical properties of concrete by homogenization method and a multiphysics approach of the damage on the cylinder head of a diesel engine. The obtained results provide the practitioner with essential informations for a significant improvement of the performance of the structure.

In this thesis we will elaborate on multivariate extreme value modelling, re- lated practical and theoretical aspects. We will mainly focus on the dependence models, the extreme value copulas in particular. Extreme value copulas effec- tively unify the univariate extreme value theory and the copula framework itself in a single view. We familiarize ourselves with both of them in the first two chapters. Those chapters present generalized extreme value distribution, gen- eralized Pareto distribution and Archimedean copulas, that are suitable for the multivariate maxima and the threshold exceedances description. These two top- ics will be addressed in the third chapter in detail. Taking into consideration rather practical focus of this thesis, we examine the methods of data analysis extensively. Furthermore, we will employ these methods in a comprehensive case study, that will aim to reveal the importance of extreme value theory application in the Catastrophe Insurance. 1