Submitted by Guilherme Almeida (gribalmeida@yahoo.com.br) on 2010-06-08T17:36:26Z No. of bitstreams: 1 Dissertação Final.pdf: 295042 bytes, checksum: 8605c5a79af832a043b920088d6f45bb (MD5) / Approved for entry into archive by Vitor Souza(vitor.souza@fgv.br) on 2010-06-16T18:54:46Z (GMT) No. of bitstreams: 1 Dissertação Final.pdf: 295042 bytes, checksum: 8605c5a79af832a043b920088d6f45bb (MD5) / Made available in DSpace on 2010-06-18T13:44:59Z (GMT). No. of bitstreams: 1 Dissertação Final.pdf: 295042 bytes, checksum: 8605c5a79af832a043b920088d6f45bb (MD5) Previous issue date: 2010-05-26 / In this paper, we use the information from the credit default swap market to measure the main components of the oil and gas companies spread. Using nearly 20 companies of this industry with different ratings and nearly 80 bonds, the result was that the majority of the oil and gas spread is due to the default risk. We also find that the spread component related to the non-default is strongly as sociated with some liquidity measures of bond markets, what suggest that liquidity has a very important role in the valuation of fixed income assets. On the other side, we do not find evidence that the non-default component of the spread is related to tax matters. / Neste trabalho, utilizamos informações do mercado de credit default swap para medir os principais componentes do spread das empresas do setor de óleo e gás. Utilizando cerca de 20 empresas da indústria de óleo e gás composta por companhias de diversos ratings e aproximadamente 80 bonds, os resultados mostraram que a maior parte do spread corporativo do setor decorre do risco de inadimplemento. Também encontramos que o componente do spread não relacionado ao default é fortemente associado a algumas medidas de liquidez do mercado de bonds, sugerindo que a liquidez tem um papel importante na avaliação de títulos de renda fixa. Por outro lado, não encontramos evidências da importância de fatores tributários na explicação do componente do spread não relacionado à inadimplência.

Radial basis function methods exhibit several very attractive properties such as a high order convergence of the approximated solution and flexibility to the domain geometry. However the method in its classical formulation becomes impractical for problems with relatively large numbers of degrees of freedom due to the ill-conditioning and dense structure of coefficient matrix. To overcome the latter issue we employ a localisation technique, namely a partition of unity method, while the former issue was previously addressed by several authors and was of less concern in this thesis. In this thesis we develop radial basis function partition of unity methods for partial differential equations arising in financial mathematics and glaciology. In the applications of financial mathematics we focus on pricing multi-asset equity and credit derivatives whose models involve several stochastic factors. We demonstrate that localised radial basis function methods are very effective and well-suited for financial applications thanks to the high order approximation properties that allow for the reduction of storage and computational requirements, which is crucial in multi-dimensional problems to cope with the curse of dimensionality. In the glaciology application we in the first place make use of the meshfree nature of the methods and their flexibility with respect to the irregular geometries of ice sheets and glaciers. Also, we exploit the fact that radial basis function methods are stated in strong form, which is advantageous for approximating velocity fields of non-Newtonian viscous liquids such as ice, since it allows to avoid a full coefficient matrix reassembly within the nonlinear iteration. In addition to the applied problems we develop a least squares radial basis function partition of unity method that is robust with respect to the node layout. The method allows for scaling to problem sizes of a few hundred thousand nodes without encountering the issue of large condition numbers of the coefficient matrix. This property is enabled by the possibility to control the coefficient matrix condition number by the rate of oversampling and the mode of refinement.

This dissertation thesis focuses on complex analysis of the problem, which is the sovereign debt crisis in the Euro area. The aim of this paper is to provide a complex overview and analysis of the current sovereign debt crisis, from the theoretical definition of the term, through an analysis of the causes and consequences of this crisis to outline the economic policy response to it. The text is divided into two parts. The first part deals with theoretical problem solving. In the second part is analyzed and described course of sovereign debt crisis. This section also analyzes in detail causes and consequences of the sovereign debt crisis in certain countries. This section is completed by an analysis of economic policy response to the sovereign debt crisis and an expert estimate of the future development of public debt countries analyzed.

Cette thèse étudie le risque de crédit souverain et son impact sur les banques et les entreprises. Le premier essai montre que le risque de crédit bancaire est lié au risque de crédit souverain via l’exposition commune au risque systémique au lieu du sauvetage implicite ou de l’exposition excessive aux obligations émises par le pays d’origine. Dans le deuxième essai, je construis un modèle de structure du capital qui prédit une corrélation négative entre le niveau d’endettement des grands entreprises et le risque de crédit souverain à cause du sauvetage implicite. Cette prédiction est confirmée en suite par des preuves empiriques des entreprises dans la zone euro. Le troisième essai donne un modèle joint de CDS et d’obligation pour identifier les composantes de défaut et de liquidité dans les spreads de CDS et les rendements obligataires. Je trouve une composante de liquidité importante dans les spreads de CDS des pays périphériques de la zone euros et conclus que le fait de ne pas prendre en compte de l’illiquidité des CDS conduit à surestimer la composante de défaut dans le rendement obligataire. / This thesis studies sovereign credit risk and its impact on banks and industrial firms. The first essay shows that bank credit risk is linked to sovereign credit risk through common exposure to systemic risk instead of implicit bailout or excessive holding of home country bonds. In the second essay, I build a trade-off model of capital structure which predicts negative correlation between optimal leverage of big firms and sovereign credit risk due to implicit bailout. The model prediction is confirmed by empirical evidence from firms in the euro area. The third essay provides a joint pricing model of CDS and bond to disentangle the default and liquidity component in CDS spread and bond yield spread. I find a remarkable liquidity component in the CDS spreads of peripheral euro area countries and conclude that ignoring CDS illiquidity leads to overestimation of default component in bond yield.

In the aftermath of the credit crisis in 2007, the importance of Credit Valuation Adjustment (CVA) rose in the Over The Counter (OTC) derivative pricing process. One important part of the pricing process is to determine Probability of Defaults (PDs) of the counterparty in question. The normal way of doing this is to use Credit Default Swap (CDS) spreads from the CDS market. In some cases, there is no associated liquid CDS market, and in those cases, it is market practice to use proxy CDS spreads. In this thesis, transformer models are used to generate proxy CDS spreads with a certain region, rating, and tenor from stand-alone CDS spread data. Two different models are created to do this. The first simpler model is an encoder-based model that uses stand-alone CDS data from a single company to generate one proxy spread per inference. The second, more advanced model is an encoder-decoder model that uses stand-alone CDS data from three companies to generate one proxy spread per inference. The performance of the models is compared, and it is shown that the more advanced model outperforms the simpler model. It should, be noted that the simpler model is faster to train. Both models could be used for data validation. To create the transformer models, it was necessary to implement custom embeddings that embedd specific corporate information and temporal information regarding the CDS spreads. The importance of the different embeddings was also investigated, and it is clear that certain embeddings are more important than others. / I efterdyningarna av kreditkrisen 2007 så ökade betydelsen av CVA vid prissättning av OTC derivat. En viktig del av prissättningen av OTC derivat är att avgöra PDs för den aktuella motparten. Om det finns en likvid CDS marknad för motparten så kan man använda sig av CDSs spreadar dirket från marknaden för att avgöra PDs. I många fall så saknas en sådan likvid CDS marknad. Då är det praksis att istället använda sig av proxy CDS spreadar. I den här uppsatsen så presenteras två transformer modeller för att generera proxy CDS spreadar för bestämda kombinationer av region, rating och löptid från enskilda företags CDS spreadar. Den först enklare modellen är en encoder baserad modell som använder sig av data från ett enskilt företag för att generera en proxy spread per inferens. Den andra modellen är en mer avancerad encoder-decoder modell. Den mer avancerade modellen använder sig av data från tre företag för att generera en proxy spread. I uppsatsen jämförs dessa modeller och man kan konstatera att den mer avancereade modellen genererar mer exakta CDS spreadar. Den enklare modellen är dock betydligt enklare att träna och båda modellerna kan användas i syfte att validera det riktiga proxy datat. För att kunna skapa modellerna så var det en nödvändighet att implementera specialbyggda embeddings som kodad in temporal information och företagsspecifik information om CDS spreadarna. Dessutom så testades vikten av enskilda embeddings och det var uppenbart att vissa embeddings var viktigare än andra.

固定期信用違約交換(Constant Maturity Credit Default Swap)是移轉固定年期信用違約交換信用價差(CDS Spread)變動風險的信用衍生性金融商品，目前僅Brigo(2005)以及Krekel and Wenzel(2006)探討固定期信用違約交換的評價，也各自推導出近似封閉解，但對於相關參數之估計以及避險參數並沒有涉及，因此本研究將利用歷史資料估計Krekel and Wenzel(2006)評價公式中的參數，讓評價模型更加完備，並求算避險參數，提供發行商與投資人避險資訊。 本文利用目前信用違約交換(Credit Default Swap)市場中各到期日流動性較高的美國Eastman Kodak Company公司債作為標的物，發行一檔固定期信用違約交換，並利用現有市場資訊估計模型中的參數。在避險實證上，本文利用標的物債券信用價差曲線的變動，對固定期信用違約交換契約價值以及五年期及十年期信用違約交換契約價值的影響，建構了一個避險投資組合，使得避險後總投資組合價值波動減少。 / Constant Maturity Credit Default Swap (CMCDS) is one of the credit derivatives, whose function is to circumvent the fluctuating risk of CDS Spread. Brigo (2005) and Krekel and Wenzel (2006) focused on not only probing into the evaluation of the CMCDS but also deriving the approximated closed-form solution in their recent research separately. However, they seldom concern the hedging approach and the estimated parameters of pricing model, which could be major variable in the measurement. This paper is aiming to calculate the history data of hazard rate to estimate the parameters by using the formula from Krekel and Wenzel (2006) and compute the hedging approach of the pricing model to make it become more complete and provide the hedging information for both financial institutions and investors. By using the corporation bond of Eastman Kodak Company which with higher liquidity and various maturity as the main reference asset to issue a CMCDS and utilizing the current available market data to estimate the parameters of the pricing model to evaluate the value of the product, I find that the various credit spread curve of reference bond will influence the value of CDS and CMCDS and try to structure a hedging portfolio to eliminate the fluctuation of the product.

本研究分為兩個部份，第一部份提出評價選擇權時，應考慮加價利益(Mark-Up Interest)的觀點，第二部份則提出信用違約交換選擇權的新評價模型。 在第一部份，所謂加價利益是指選擇權賣方為彌補採取避險組合後仍可能發生的損失而向選擇權買方收取的風險補償。本研究的方法是將選擇權市價拆解成理論公平賭局價格與加價利益，建立包含加價利益、買賣權平價理論、隱含標的價格與猜測波動度的選擇權評價模型，解決隱含波動度微笑(implied volatility smile)所帶來模型內部不一致的問題。在建立各種情境條件下之加價利益後，可用來評估選擇權市價的合理性，以提升買賣雙方對市價的合理判斷，有利於風險管理者進行選擇權之造市操作與避險。本研究經由對台指選擇權(TXO)的實證結果發現：加價利益受到距到期交易日、價況程度(moneyness)及猜測波動度的影響。 第二部份所提出之信用違約交換選擇權的新評價模型則是延伸Schonbucher ( 2000, 2003, 2004 )、Brigo ( 2004, 2005a, 2005b, 2006 )、Brigo & Mercurio ( 2006 )、Brigo & Morini ( 2005 )、Jamshidian ( 2004 ) 與Wu ( 2006 ) 的研究，以市場上交易之各年期信用違約交換之商品所導出之費率期間內之各單期( single tenor )遠期信用違約交換率之費率端價值做為計價資產，假設各單期遠期違約交換率為對數常態分配下，可以將信用違約交換選擇權拆解為由各單期加總之違約交換選擇權，應用在投資銀行發行許多相同標的但不同起始日、不同到期日之一系列信用違約交換選擇權( CDS options )時，可以具有評價簡易的優勢，吻合各期間之信用市場狀況，避免套利機會，並能運用信用違約交換( CDS )，增進避險與管理信用風險之技術。 / This thesis is composed of two parts. The first part is the standpoint of the “Mark-Up Interest” on options. The second part is the new model about pricing and hedging on credit default swap options. In the first part, the Mark-Up Interest is regarded as the reward on the hedging portfolio to compensate for possible losses. For presenting this, options market prices are decomposed into the fair-game options prices and the Mark-Up Interests. The options pricing model formed with the Mark-Up Interest, put-call parity, implied underlying price, and guessed volatility is used to solve the internal inconsistence caused by the implied volatility smiles. Therefore, the justness of the options market prices could be estimated with the Mark-Up Interests under different scenarios. The result will help the risk manager to do market making and hedging. The empirical results based on the Options on Taiwan Stock Exchange Weighted Stock Index (TXO) in this paper are as follows: The trading days to expiry, moneyness, and guessed volatility are the factors affecting the Mark-Up Interests. The second part of this thesis extends the research on Schonbucher ( 2000, 2003, 2004 ), Brigo ( 2004, 2005a, 2005b, 2006 ), Brigo & Mercurio ( 2006 )、Brigo & Morini ( 2005 ), Jamshidian ( 2004 ) and Wu ( 2006 ). We use the fee leg of the single tenor forward credit default swap rate ( tenor CDS rate ) as numeraire. Under the lognormal distribution assumption on the tenor CDS rate, we decompose a credit default swap option into the sum of tenor CDS options. The result can be used by investment banks to manage credit risk when their derivative book consists of different start-date and end-date CDS options. In addition, our result shows that CDS can be used to hedge against the risk of CDS options. The proposed method helps improve the techniques of hedging and managing credit risk.

Diese Dissertation konzentriert sich auf das hochdimensionale Financial Engineering, insbesondere in der Dependenzmodellierung und der sequentiellen Überwachung. Im Bereich der Dependenzmodellierung wird eine Einführung hochdimensionaler Kopula vorgestellt, die sich auf den Stand der Forschung in Kopula konzentriert. Eine komplexere Anwendung im Financial Engineering, bei der eine hochdimensionale Kopula verwendet wird, konzentriert sich auf die Bepreisung von Portfolio-ähnlichen Kreditderivaten, d. h. CDX-Tranchen (Credit Default Swap Index). In diesem Teil wird die konvexe Kombination von Kopulas in der CDX-Tranche mit Komponenten aus der elliptischen Kopula-Familie (Gaussian und Student-t), archimedischer Kopula-Familie (Frank, Gumbel, Clayton und Joe) und hierarchischer archimedischer Kopula-Familie vorgeschlagen. Im Abschnitt über finanzielle Überwachung konzentriert sich das Kapitel auf die Überwachung von hochdimensionalen Portfolios (in den Dimensionen 5, 29 und 90) durch die Entwicklung eines nichtparametrischen multivariaten statistischen Prozesssteuerungsdiagramms, d.h. eines Energietest-basierten Kontrolldiagramms (ETCC). Um die weitere Forschung und Praxis der nichtparametrischen multivariaten statistischen Prozesskontrolle zu unterstützen, die in dieser Dissertation entwickelt wurde, wird ein R-Paket "EnergyOnlineCPM" entwickelt. Dieses Paket wurde im Moment akzeptiert und veröffentlicht im Comprehensive R Archive Network (CRAN), welches das erste Paket ist, das die Verschiebung von Mittelwert und Kovarianz online überwachen kann. / This dissertation focuses on the high dimensional financial engineering, especially in dependence modeling and sequential surveillance. In aspect of dependence modeling, an introduction of high dimensional copula concentrating on state-of-the-art research in copula is presented. A more complex application in financial engineering using high dimensional copula is concentrated on the pricing of the portfolio-like credit derivative, i.e. credit default swap index (CDX) tranches. In this part, the convex combination of copulas is proposed in CDX tranche pricing with components stemming from elliptical copula family (Gaussian and Student-t), Archimedean copula family (Frank, Gumbel, Clayton and Joe) and hierarchical Archimedean copula family used in some publications. In financial surveillance part, the chapter focuses on the monitoring of high dimensional portfolios (in 5, 29 and 90 dimensions) by development of a nonparametric multivariate statistical process control chart, i.e. energy test based control chart (ETCC). In order to support the further research and practice of nonparametric multivariate statistical process control chart devised in this dissertation, an R package "EnergyOnlineCPM" is developed. At moment, this package has been accepted and published in the Comprehensive R Archive Network (CRAN), which is the first package that can online monitor the shift in mean and covariance jointly.

Credit risk measurement and management has great importance in credit market. Credit derivative products are the major hedging instruments in this market and credit default swap contracts (CDSs) are the most common type of these instruments. As observed in credit crunch (credit crisis) that has started from the United States and expanded all over the world, especially crisis of Iceland, CDS premiums (prices) are better indicative of credit risk than credit ratings. Therefore, CDSs are important indicators for credit risk of an obligor and thus these products should be understood by market participants well enough. In this thesis, initially, advanced credit risk models firsts, the structural (firm value) models, Merton Model and Black-Cox constant barrier model, and the intensity-based (reduced-form) models, Jarrow-Turnbull and Cox models, are studied. For each credit risk model studied, survival probabilities are calculated. After explaining the basic structure of a single name CDS contract, by the help of the general pricing formula of CDS that result from the equality of in and out cash flows of these contracts, CDS price for each structural models (Merton model and Black-Cox constant barrier model) and CDS price for general type of intensity based models are obtained. Before the conclusion, default intensities are obtained from the distribution functions of default under two basic structural models / Merton and Black-Cox constant barrier. Finally, we conclude our work with some inferences and proposals.

In this thesis, the structural model in credit risk and the credit derivatives is studied under both Black-Scholes setting and Variance Gamma (VG) setting. Using a Variance Gamma process, the distribution of the firm value process becomes asymmetric and leptokurtic. Also, the jump structure of VG processes allows random default times of the reference entities. Among structural models, the most emphasis is made on the Black-Cox model by building a relation between the survival probabilities of the Black-Cox model and the value of a binary down and out barrier option. The survival probabilities under VG setting are calculated via a Partial Integro Differential Equation (PIDE). Some applications of binary down and out barrier options, default probabilities and Credit Default Swap par spreads are also illustrated in this study.