This dissertation analyzes key features of credit derivatives market, basic risks of the products and trends the market has experienced for several years since its inception, discusses regulatory issues of the market with regard to the Basel II treatment and key reasons for investors using credit derivatives. Dissertation also examines whether and how credit derivatives affected current financial turmoil, analyzes credit derivatives losses of selected institutions on the financial markets and compares them with total losses of these institutions. The main result of the work is that there was no substantial effect of the credit derivatives market on the current financial crisis. Dissertation also examines whether there is any connection between U.S. banks credit derivatives trades and their capital adequacy ratio. According to the analysis, there is no evidence for credit derivatives to essentially affect capital adequacy ratio of U.S. banks. A potential explanation for the higher values of U.S. banks' capital adequacy ratio may be that there are sophisticated risk management strategies banks have been implicating for many years.

A presente tese objetiva estudar o Credit Default Swap (CDS) e o Total Return Swap (TRS), que são os derivativos de crédito cuja negociação é permitida no país. Analisaremos a utilização destes instrumentos financeiros no sistema bancário, seus efeitos deletérios no mercado financeiro, o modo como são regulados no direito brasileiro, bem como as recentes alterações legislativas nos Estados Unidos e União Europeia pós crise de 2008. / This thesis aims at studying the Credit Default Swap (CDS) and the Total Return Swap (TRS), which are credit derivatives whose negotiation is permitted in the country. We will analyze the use of these financial instruments in the banking system, its deleterious effects on the financial market, the way they are regulated in Brazilian law, as well as the recent legislative changes in the United States and European Union after the 2008 crisis.

The credit derivatives market has known an incredible development since its advent in the 1990's. Today there is a plethora of credit derivatives going from the simplest ones, credit default swaps (CDS), to more complex ones such as synthetic single-tranche collateralized debt obligations. Valuing this rich panel of products involves modeling credit risk. For this purpose, two main approaches have been explored and proposed since 1976. The first approach is the Structural approach, first proposed by Merton in 1976, following the work of Black-Scholes for pricing stock options. This approach relies in the capital structure of a firm to model its probability of default. The other approach is called the Reduced-form approach or the hazard rate approach. It is pioneered by Duffie, Lando, Jarrow among others. The main thesis in this approach is that default should be modeled as a jump process. The objective of this work is to value Asset-backed Credit default swaps using the hazard rate approach.

Credit derivatives are among the most criticized financial instruments in the current credit crises. Given their short history, finance professionals are still researching to discover effective ways to reduce the mark-to-market (MTM) volatility in credit derivatives, especially in turbulent market conditions. Many credit portfolios have been struggling to find out appropriate tools and techniques to help them navigate the current credit crises and hedge mark-to-market volatility in their portfolios. In this study we provide a tool kit to help reduce the pricing fluctuations in structured credit portfolios utilizing data analysis and statistical methods. In Chapter One we provide a snapshot of credit derivatives market by summarizing different types of credit derivatives; including single-name credit default swaps (CDS), market credit indices, bespoke portfolios, market index tranches, and bespoke tranches (synthetic CDOs). In Chapter Two we illustrate a method to calculate a stable hedge ratio (beta) by combining industry practices and statistical techniques. Choosing an appropriate hedge ratio is critical for funds that desire to hedge mark-to-market volatility. Many credit portfolios suffered 40%-80% market value losses in 2008 and 2009 due to the mark-to-market volatility in their long positions. In this chapter we introduce ten different betas in order to hedge a long bespoke portfolio by liquid market indices. We measure the effectives of these betas by two measures: Stability and mark-to-market volatility reduction. Among all betas we present, we deduct that the following betas are appropriate to be used as hedge ratios: Implied Beta, Quarterly Regression Beta on Spread Levels, Yearly Regression Betas on Spread Levels, Up Beta, and Down Beta. In Chapter Three we analyze the risk factors that impact the MTM volatility in CDS tranches; namely Spread Risk, Correlation Risk, Dispersion Risk, and Curve Risk. We focus our analysis in explaining the risks in the equity tranche as this is the riskiest tranche in the capital structure. We show that all four risks introduced are critical in explaining MTM volatility in equity tranches. We also perform multiple regression analysis to show the correlations between different risk factors. We show that, when combined, spread, correlation, and dispersion risks are the most important risk factors in analyzing MTM fluctuations in equity tranche. Curve risk can be used as an add-on risk to further explain local instances. After understanding various risk factors that impact the MTM changes in equity tranche, we put this knowledge to work to analyze two instances in 2008 in which we experienced significant spread widening in equity tranche. Both examples show that a good understanding of the risks that drive MTM changes in CDS tranches is critical in making informed trading decisions. In Chapter Four we focus on two topics: Portfolio Stratification and Index Selection. While portfolio stratification helps us better understand the composition of a portfolio, index selection shows us which indices are more suitable in hedging long bespoke positions. In stratifying a portfolio we define Class-A as the widest credits, Class-B as the middle tier, and Class-C as the tightest credits in a credit portfolio. By portfolio stratification we show that Class-A has significant impact on the overall portfolio. We use five different risk measures to analyze different properties of the three classes we introduce. The risk measures are Sum of Spreads (SOS), Sigma/Mu, Basis Point Volatility (BPVOL), Skewness, and Kurtosis. For all risk measures we show that there is high correlation between Class-A and the whole portfolio. We also show that it is critical to monitor the risks in Class-A to better understand the spread moves in the overall portfolio. In the second part of Chapter Four, we perform analysis to find out which credit index should be used in hedging a long bespoke portfolio. We compare four credit indices for their ability to track the bespoke portfolio on spread levels and on spread changes. Analysis show that CDX.HY and CDX IG indices fits the best to hedge our sample bespoke portfolio in terms of spread levels and spread changes, respectively. Finally, we perform multiple regression analysis using backward selection, forward selection, and stepwise regression methods to find out if we should use multiple indices in our hedging practices. Multiple regression analysis show that CDX.HY and CDX.IG are the best candidates to hedge the sample bespoke portfolio we introduced.

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Thesis (doctoral)--Universität, Frankfurt. / Includes bibliographical references (p. 131-135).

In this thesis, efforts are devoted to the stochastic modeling, measurement and evaluation of credit risks, the development of mathematical and statistical tools to estimate and predict these risks, and methods for solving the significant computational problems arising in this context. The reduced-form intensity based credit risk models are studied. A new type of reduced-form intensity-based model is introduced, which can incorporate the impacts of both observable trigger events and economic environment on corporate defaults. The key idea of the model is to augment a Cox process with trigger events. In addition, this thesis focuses on the relationship between structural firm value model and reduced-form intensity based model. A continuous time structural asset value model for the asset value of two correlated firms with a two-dimensional Brownian motion is studied. With the incomplete information introduced, the information set available to the market participants includes the default time of each firm and the periodic asset value reports. The original structural model is first transformed into a reduced-form model. Then the conditional distribution of the default time as well as the asset value of each name are derived. The existence of the intensity processes of default times is proven and explicit form of intensity processes is given in this thesis. Discrete-time Markovian models in credit crisis are considered. Markovian models are proposed to capture the default correlation in a multi-sector economy. The main idea is to describe the infection (defaults) in various sectors by using an epidemic model. Green’s model, an epidemic model, is applied to characterize the infectious effect in each sector and dependence structures among various sectors are also proposed. The models are then applied to the computation of Crisis Value-at-Risk (CVaR) and Crisis Expected Shortfall (CES). The relationship between correlated defaults of different industrial sectors and business cycles as well as the impacts of business cycles on modeling and predicting correlated defaults is investigated using the Probabilistic Boolean Network (PBN). The idea is to model the credit default process by a PBN and the network structure can be inferred by using Markov chain theory and real-world data. A reduced-form model for economic and recorded default times is proposed and the probability distributions of these two default times are derived. The numerical study on the difference between these two shows that our proposed model can both capture the features and fit the empirical data. A simple and efficient method, based on the ordered default rate, is derived to compute the ordered default time distributions in both the homogeneous case and the two-group heterogeneous case under the interacting intensity default contagion model. Analytical expressions for the ordered default time distributions with recursive formulas for the coefficients are given, which makes the calculation fast and efficient in finding rates of basket CDSs. / published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy

Background: The financial crisis of 2007-2010 had a massive impact on the financial markets worldwide. The crisis was partly blamed on the credit derivatives collateralized debt obligations and credit default swaps. These instruments were used to create leverage and speculation, which led to uncertainty in the financial system worldwide. There has been no recent documentation of how credit derivatives are used in Swedish banks, and what risks and opportunities they bring along. Purpose: The purpose of this thesis is to describe the use of credit derivatives in Swedish banks, what benefits and risks they may generate and how the recent financial crisis has affected their use. Research Method: This is a qualitative multiple case study which uses an inductive approach. The study covers four cases, three of the largest Swedish commercial banks, and a bank that specializes on international financing. Seven people working in different fields in these banks have been interviewed. Conclusions: Credit derivatives are mostly used for hedging in Swedish banks, which mainly involves the use of credit default swaps, and sometimes iTraxx. Purely speculative trades are rare. The risks that arise are mainly due to lack of transparency in OTC trading, and abusive use of these instruments. Credit derivatives greatly facilitate risk management in banks. Regulations have increased since the financial crisis and the demand for more complex products greatly decreased.

A credit derivative is a financial instrument whose value depends on the credit risk of an underlying asset or assets. Credit risk is the possibility that the obligor fails to honor any payment obligation. This thesis proposes four new computational methods for the valuation of credit derivatives. Compared with synthetic collateralized debt obligations (CDOs) or basket default swaps (BDS), the value of which depends on the defaults of a prescribed underlying portfolio, a forward-starting CDO or BDS has a random underlying portfolio, as some ``names'' may default before the CDO or BDS starts. We develop an approach to convert a forward product to an equivalent standard one. Therefore, we avoid having to consider the default combinations in the period between the start of the forward contract and the start of the associated CDO or BDS. In addition, we propose a hybrid method combining Monte Carlo simulation with an analytical method to obtain an effective method for pricing forward-starting BDS. Current factor copula models are static and fail to calibrate consistently against market quotes. To overcome this deficiency, we develop a novel chaining technique to build a multi-period factor copula model from several one-period factor copula models. This allows the default correlations to be time-dependent, thereby allowing the model to fit market quotes consistently. Previously developed multi-period factor copula models require multi-dimensional integration, usually computed by Monte Carlo simulation, which makes the calibration extremely time consuming. Our chaining method, on the other hand, possesses the Markov property. This allows us to compute the portfolio loss distribution of a completely homogeneous pool analytically. The multi-period factor copula is a discrete-time dynamic model. As a first step towards developing a continuous-time dynamic model, we model the default of an underlying by the first hitting time of a Wiener process, which starts from a random initial state. We find an explicit relation between the default distribution and the initial state distribution of the Wiener process. Furthermore, conditions on the existence of such a relation are discussed. This approach allows us to match market quotes consistently.

A credit derivative is a financial instrument whose value depends on the credit risk of an underlying asset or assets. Credit risk is the possibility that the obligor fails to honor any payment obligation. This thesis proposes four new computational methods for the valuation of credit derivatives. Compared with synthetic collateralized debt obligations (CDOs) or basket default swaps (BDS), the value of which depends on the defaults of a prescribed underlying portfolio, a forward-starting CDO or BDS has a random underlying portfolio, as some ``names'' may default before the CDO or BDS starts. We develop an approach to convert a forward product to an equivalent standard one. Therefore, we avoid having to consider the default combinations in the period between the start of the forward contract and the start of the associated CDO or BDS. In addition, we propose a hybrid method combining Monte Carlo simulation with an analytical method to obtain an effective method for pricing forward-starting BDS. Current factor copula models are static and fail to calibrate consistently against market quotes. To overcome this deficiency, we develop a novel chaining technique to build a multi-period factor copula model from several one-period factor copula models. This allows the default correlations to be time-dependent, thereby allowing the model to fit market quotes consistently. Previously developed multi-period factor copula models require multi-dimensional integration, usually computed by Monte Carlo simulation, which makes the calibration extremely time consuming. Our chaining method, on the other hand, possesses the Markov property. This allows us to compute the portfolio loss distribution of a completely homogeneous pool analytically. The multi-period factor copula is a discrete-time dynamic model. As a first step towards developing a continuous-time dynamic model, we model the default of an underlying by the first hitting time of a Wiener process, which starts from a random initial state. We find an explicit relation between the default distribution and the initial state distribution of the Wiener process. Furthermore, conditions on the existence of such a relation are discussed. This approach allows us to match market quotes consistently.