A credit default swap is a contract that ensures protection against losses occurring due to a default event of an certain entity. It is crucial to know how default should be modelled for valuation or estimating of credit derivatives. In this dissertation, we first review the structural approach for modelling credit risk. The model is an approach for assessing the credit risk of a firm by typifying the firms equity as a European call option on its assets, with the strike price (or exercise price) being the promised debt repayment at the maturity. The model can be used to determine the probability that the firm will default (default probability) and the Credit Spread. We second concentrate on the valuation of credit derivatives, in particular the Credit Default Swap (CDS) when the hazard rate (or even of default) is modelled as the Vasicek-type model. The other objective is, by using South African credit spread data on defaultable bonds to estimate parameters on CIR and Vasicek-type Hazard rate models such as stochastic differential equation models of term structure. The parameters are estimated numerically by the Moment Method. / Thesis (M.Sc.)-University of KwaZulu-Natal, Durban, 2013.

Made available in DSpace on 2016-04-26T20:48:49Z (GMT). No. of bitstreams: 1 Marcos Ricardo Carnelos.pdf: 425491 bytes, checksum: af0e9c611cb4dca4d99f0e8cc5c928f8 (MD5) Previous issue date: 2007-10-30 / The aim of this work is to analyze the dynamic of the evolution of new financial products called credit derivatives. The purpose of this analysis is to provide a better comprehension of the transformation process of the financial products, mainly those related to management of credit portfolios, as well as, to show the advantages that these products can offer to the Brazilian market. The focus of this work is on the national market, which is at its early stage of development, still having little liquidity, however, the international market of these products is very large and every day new products are developed. The work also shows the applicability of different kinds of credit derivatives and the way these products should be handled / Esse trabalho objetivou analisar a dinâmica da evolução de uma nova classe de instrumentos financeiros chamados de derivativos de crédito. Essa análise tem como objetivo fornecer uma melhor compreensão do processo de transformação dos produtos financeiros, principalmente aqueles relacionados ao gerenciamento de carteiras de crédito, bem como analisar as vantagens que tais produtos podem oferecer para o mercado brasileiro. O foco desse trabalho é o mercado nacional, entretanto é possível verificar que embora o mercado mundial desses instrumentos seja grande e a cada dia desenvolvem-se novos produtos, no Brasil esses instrumentos estão em fase inicial de desenvolvimento, tendo ainda pouca liquidez. O trabalho mostra também a aplicabilidade dos diferentes tipos de derivativos de crédito e de que forma esses instrumentos devem ser tratados

信用風險對銀行、債券發行者及債券投資者而言是個很重要的考量，因此信用風險的管理成為一個很重要的課題。但管理信用風險的傳統方法，對控制信用風險都只能解決部分的問題。信用衍生性商品便應運而生。 評價信用衍生性商品的首要工作為對信用風險予以衡量及評價。本文採用違約強度模型評價信用風險並將其應用至信用價差選擇權的評價，試圖提供信用價差選擇權的合理價值及該評價公式在現實生活的可行性，並討論相關變數變動對信用價差選擇權價值的影響。 / Credit risk is an important consideration for banks, bond issuers, and bond investors. The conventional methods of managing credit risk, such as diversification, bank loan sales, and asset securitization, offer only a partial solution to controlling credit risk exposure. In recent years, the growing market for credit derivatives has provided powerful new tools for managing credit risk that can be less costly and more effective than traditional methods. How to measure and value credit risk is the main task of credit derivatives. The present study adopts an intensity model to value credit risk and applies this approach to price credit spread options. This study provides the reasonable premium for credit spread options and the practice of the pricing formula in the real world. It also covers the effects of the put premium for credit spread concerning the related variables.

Incomplete markets provide many challenges for both investment decisions and valuation problems. While both problems have received extensive attention in complete markets, there remain many open areas in the theory of incomplete markets. We present the results in three parts. In the first essay we consider the Merton investment problem of optimal portfolio choice when the traded instruments are the set of zero-coupon bonds. Working within a Markovian Heath-Jarrow-Morton framework of the interest rate term structure driven by an infinite dimensional Wiener process, we give sufficient conditions for the existence and uniqueness of an optimal investment strategy. When there is uniqueness, we provide a characterization of the optimal portfolio. Furthermore, we show that a specific Gauss-Markov random field model can be treated within this framework, and explicitly calculate the optimal portfolio. We show that the optimal portfolio in this case can be identified with the discontinuities of a certain function of the market parameters. In the second essay we price a claim, using the indifference valuation methodology, in the model presented in the first section. We appeal to the indifference pricing framework instead of the classic Black-Scholes method due to the natural incompleteness in such a market model. Because we price time-sensitive interest rate claims, the units in which we price are very important. This will require us to take care in formulating the investor’s utility function in terms of the units in which we express the wealth function. This leads to new results, namely a general change-of-numeraire theorem in incomplete markets via indifference pricing. Lastly, in the third essay, we propose a method to price credit derivatives, namely collateralized debt obligations (CDOs) using indifference. We develop a numerical algorithm for pricing such CDOs. The high illiquidity of the CDO market coupled with the allowance of default in the underlying traded assets creates a very incomplete market. We explain the market-observed prices of such credit derivatives via the risk aversion of investors. In addition to a general algorithm, several approximation schemes are proposed. / text

過去數年來，隨著金融市場的逐漸開放，帶動了整個金融市場的蓬勃發展。不過，隨之而來的風險，也產生了不少的金融災難。而這些的金融災難，大多是由於金融商品投資避險上的操作不當，或者是風險控管失衡所造成的。為了避免如是情況再度發生，近年來，國際間相繼有許多學者投入風險管理的研究。 而在所有的產業之中，風險管理對於銀行業來說，更為重要。銀行作為產業的金融媒介，一旦發生金融災難，不只產業會受到衝擊，連帶地資金來源的存款戶也受害，影響層面極為廣大。所以，各國政府莫不對銀行業設有相當嚴格的管理規定，以健全整體金融環境的發展。例如，有名的巴塞爾資本協定，即為國際間對於金融環境的風險管理規範。 但是，隨著時空環境的變遷，原有的協定早以不敷需求。終於，在2004年中，巴塞爾銀行監理委員會公佈了定版的新巴塞爾資本協定，並決定於2006年底開始實施。新協定在原有資本準備方面，將作業風險納入風險評估的範圍，並大幅修訂信用風險的衡量方式，允許銀行使用自行開發的內部模型，並採認降低信用風險的工具。而且，更增加了監理審查程序及市場紀律的相關規定，期待以多方面的角度，強化國際金融體系。 本研究將由新巴塞爾資本協定談起，簡介新協定的相關內容，比較新舊協定不同之處，然後針對銀行主要面臨的信用風險部分，探討在新協定所允許使用的信用風險內部模型，以及信用風險抵減技術。分別介紹目前業界常見的四種信用風險模型：專業信用分析公司KMV的KMV模型、CSFP的CreditRisk+模型、J.P. Morgan的CreditMetrics™模型、McKinsey的CreditPortfolioView模型，以及信用衍生性商品與信用風險證券化概念，最後探討未來風險管理發展的可能方向。

Cette thèse étudie la dynamique du marché des credit default swaps (CDS), instruments financiers de transfert du risque du crédit, et de ses relations avec les autres marchés, en particulier durant les épisodes de crise. Le marché des CDS a connu un développement vigoureux depuis son émergence, au milieu des années 90. Les volumes de contrats de CDS échangés ont augmenté à un rythme rapide, ce marché a ainsi connu le développement le plus rapide parmi les dérivés négociés de gré-à-gré (over-the-counter – OTC). Les participants de marché, principalement les grandes banques, ont su tirer parti des possibilités offertes par les outils de transfert de risque qui leur ont permis tout d'abord, de disposer d'instruments novateurs de protection contre le risque de crédit, mais aussi d'assurer l'expansion de leur activité d'intermédiation du crédit tout en optimisant les exigences en capital. Bien que le fonctionnement du marché des CDS ait connu une amélioration depuis le début des années 2000, plusieurs éléments mettent en doute l'hypothèse d'un marché efficient et résilient aux périodes de crise. A travers cinq articles empiriques, cette thèse se penche sur deux épisodes de crises durant lesquels le fonctionnement de ce marché a pu être perturbé : d'une part la crise de mai 2005, provoquée par la dégradation en catégorie spéculative de deux entreprises américaines majeures, General Motors et Ford, par les principales agences de notation ; d'autre part la crise financière ayant débuté en 2007 et qui a évolué en crise de la dette souveraine dans le cas des Etats européens à partir de fin 2009. L'étude de ces deux phases de crise montre que le développement du marché des CDS a participé à modifier les relations entre marchés, les investisseurs ayant fait des primes de CDS une source d'information privilégiée pour évaluer le risque de crédit. En effet, les travaux empiriques menés tout au long de la thèse concluent que ce marché est devenu progressivement le lieu où tendait à se dérouler le processus de découverte des prix. Ces travaux mettent également en lumière les vulnérabilités du marché des CDS, renforcées par des effets de contagion déjà à l'œuvre lors de l'épisode de crise de 2005, et incitent à une meilleure régulation des outils de transfert du risque de crédit et, d'une manière plus générale, des dérivés OTC. / This thesis studies the dynamics of the market in credit default swaps (CDS), which are credit risk transfer instruments, and the relationships between the CDS market and other markets, particularly during crisis periods. The CDS market has seen a boom since its emergence, in the mid-90s, and volumes of CDS contracts have increased at a rapid pace. Its growth has thus been the strongest among over-the-counter (OTC) derivatives. Market participants, mainly the major banks, have taken advantage of the opportunities created by credit transfer instruments, which have offered new ways to hedge against credit risk and also contributed to the expansion of their credit intermediation activity, while optimising capital requirements. Despite the improvement of the CDS market's functioning since the early 2000s, several facts call the assumption of an efficient market that is resilient to crisis periods into question. Through five empirical articles, this thesis focuses on two crisis periods which during which the functioning of this market was affected: first, the General Motors and Ford crisis in 2005 following the downgrading of the credit ratings of these two flagship companies to speculative grade; and second, the financial crisis of 2007-2009 which turned into a sovereign debt crisis in the case of European countries from end-2009 onwards. The study of these two crisis periods shows that the growth of the CDS market has contributed to a change in the relationships between markets, as investors tend to regard CDS premia as a prime source of information to assess credit risk. Indeed, the empirical research conducted throughout the thesis concludes that this has gradually become the place where the price discovery process tends to occur. This work highlights the vulnerabilities of the CDS market, reinforced by the contagion effects at work during the 2005 crisis episode, and points to the need for better regulation of credit risk transfer instruments and, more broadly, of OTC derivatives.

Submitted by Guilherme Candido (gui0488@hotmail.com) on 2018-03-07T00:37:23Z No. of bitstreams: 1 Dissertação - Guilherme Amaral Candido.pdf: 2626690 bytes, checksum: 1e894027eeaf3360d910fb69a4a1f0b2 (MD5) / Approved for entry into archive by Thais Oliveira (thais.oliveira@fgv.br) on 2018-03-07T23:11:03Z (GMT) No. of bitstreams: 1 Dissertação - Guilherme Amaral Candido.pdf: 2626690 bytes, checksum: 1e894027eeaf3360d910fb69a4a1f0b2 (MD5) / Made available in DSpace on 2018-03-08T13:03:44Z (GMT). No. of bitstreams: 1 Dissertação - Guilherme Amaral Candido.pdf: 2626690 bytes, checksum: 1e894027eeaf3360d910fb69a4a1f0b2 (MD5) Previous issue date: 2018-02-07 / Extensa literatura existe acerca de apreçamento de derivativos de crédito, em especial Credit Default Swaps, porém pouco foi discutido sobre o caso peculiar brasileiro, com convenções de taxas de juros e legislação específicas. Este trabalho foca na implementação de um modelo de intensidade, em particular o modelo padrão da ISDA, adaptado à um contrato de CDS no Brasil sobre um emissor corporativo. Spreads de Credit Default Swaps negociados no mercado offshore, yields de bonds e yields de debêntures foram utilizados como insumos para obtenção das taxas implícitas de intensidade de default e backtesting do modelo. Os dados utilizados compreendem o período de 2015 a 2017, englobando momentos de estresse relacionados à crise política brasileira. Algumas aplicações são, então, apresentadas, entre elas hedging, basis trading e estruturação de Credit Linked Notes. / Extensive literature exists on the pricing of credit derivatives, particularly Credit Default Swaps, yet little has been discussed about the distinctive Brazilian case, with specific legislation and interest rate conventions. This work aims to implement an intensity model, in particular the standard ISDA model, adapted to a CDS contract in Brazil on a corporate issuer. Spreads of Credit Default Swaps traded in the offshore market, offshore bond yields and local bond yields were used as inputs for obtaining the implicit hazard rates and for back testing the model. The data used cover the period from 2015 to 2017, including relevant moments of stress related to the Brazilian political crisis. Some applications are then presented, including hedging, basis trading and Credit Linked Notes structuring.

The aim of this thesis is to shed more light into practical challenges related to pricing of contingent convertibles by empirically evaluating validity of two most crucial modelling assumptions of contingent convertible pricing framework. First assumption is that contractually specified capital ratio can be proxied by stock price level. Second modelling assumption is that volatility smile characteristic for stock market can be also incorporated into the contingent pricing model. First assumption is tested by comparison of probability of conversion implied by balance sheet figures with probability implied by market spreads. Analysis of our dataset indicates that probability implied by figures reported on balance sheet of issuer is statistically higher than probability estimated by market participants, suggesting that there is a confidence that reported figures do not fully represent the capital position of issuer and its ability to raise additional capital and revert the potential conversion. New information available on balance sheet also does not tend to immediately and fully materialize in contingent convertibles market. Secondly, incorporation of volatility smile characteristic for stock market leads to very low and unstable trigger level compared to level implied by balance sheet. Finally,...

With the exception of holders of default-free instruments, a key risk run by investors is credit risk. To meet the need of investors to hedge this risk, the market uses credit derivatives. The South African credit derivatives market is still in its infancy and only the very simplistic instruments are traded. One of the reasons is due to the technical sophistication required in pricing these instruments. This dissertation introduces the key concepts of risk neutral probabilities, arbitrage free pricing, martingales, default probabilities, survival probabilities, hazard rates and forward spreads. These mathematical concepts are then used as a building block to develop pricing formulae which can be used to infer valuations to the most popular credit derivatives in the South African financial markets. / Operations Research / M.Sc. (Operations Research)

Le premier volet de cette thèse traite de l’évaluation du risque de crédit. Après un chapitre introductif offrant une synthèse technique des modèles de risque, nous nous intéressons à la modélisation de la dépendance entre les risques de défaut par les copules qui permettent de mieux fonder les mesures du risque de crédit. Ces dernières assurent une description intégrale de la structure de dépendance et ont l’avantage d’exprimer la distribution jointe en termes des distributions marginales. Nous les appréhendons en termes probabilistes telles qu’elles sont désormais familières, mais également selon des perspectives algébriques, démarche à certains égards plus englobante que l’approche probabiliste. Ensuite, nous proposons un modèle général de pricing des dérivés de crédit inspiré des travaux de Cherubini et Luciano (2003) et de Luciano (2003). Nous évaluons un Credit Default Swap « vulnérable », comprenant un risque de contrepartie. Nous y intégrons la Credit Valuation Adjustment (CVA)préconisée par Bâle III pour optimiser l’allocation du capital économique. Nous reprenons la représentation générale de pricing établie par Sorensen et Bollier (1994) et contrairement aux travaux cités ci-dessus, le paiement de protection ne survient pas forcément à l’échéance du contrat. La dépendance entre le risque de contrepartie et celui de l’entité de référence est approchée par les copules. Nous examinons la vulnérabilité du CDS pour des cas de dépendance extrêmes grâce à un choix de copule mixte combinant des copules usuelles « extrêmes ». En variant le rho de Spearman, la copule mixte balaie un large spectre de dépendances, tout en assurant des closed form prices. Le modèle qui en résulte est adapté aux pratiques du marché et facile à calibrer.Nous en fournissons une application numérique. Nous mettons ensuite en évidence le rôle des dérivés de crédit en tant qu’instruments de couvertures mais aussi comme facteurs de risque, accusés d’être à l’origine de la crise des subprime. Enfin, nous analysons cette dernière ainsi que celle des dettes souveraines, héritant également de l’effondrement du marché immobilier américain. Nous proposons à la suite une étude de soutenabilité de la dette publique des pays périphériques surendettés de la zone euro à l’horizon 2016. / The first part of this thesis deals with the valuation of credit risk. After an introductory chapter providing a technical synthesis of risk models, we model the dependence between default risks with the copula that helps enhancing credit risk measures. This technical tool provides a full description of the dependence structure; one could exploit the possibility of writing any joint distribution function as a copula, taking as arguments the marginal distributions. We approach copulas in probabilistic terms as they are familiar nowadays, then with an algebraic approach which is more inclusive than the probabilistic one. Afterwards, we present a general credit derivative pricing model based on Cherubini and Luciano (2003) and Luciano (2003). We price a “vulnerable”Credit Default Swap, taking into account a counterparty risk. We consider theCredit Valuation Adjustment (CVA) advocated by Basel III to optimize theeconomic capital allocation. We recover the general representation of aproduct with counterparty risk which goes back to Sorensen and Bollier (1994)and differently from the papers mentioned above, the payment of protectiondoes not occur necessarily at the end of the contract. We approach the dependence between counterparty risk and the reference credit’s one with the copula. We study the sensitivity of the CDS in extreme dependence cases with a mixture copula defined in terms of the “extreme” ones. By varying the Spearman’s rho, one can explore the whole range of positive and negative association. Furthermore, the mixture copula provides closed form prices. Our model is then closer to the market practice and easy to implement. Later on, we provide an application on credit market data. Then, we highlight the role of credit derivatives as hedging instruments and as risk factors as well since they are accused to be responsible for the subprime crisis. Finally, we analyze the subprime crisis and the sovereign debt crisis which arose from the U.S. mortgage market collapse as well. We then study the public debt sustainability of the heavily indebted peripheral countries of the eurozone by 2016.