Dissertations / Theses on the topic 'Credit valuation adjustment (cva)'

This thesis is intended to give an overview of creditvaluation adjustment (CVA) and adjacent concepts. Firstly, the historicalevents that preceded the initiative to reform the Basel regulations and tointroduce CVA as a core component of counterparty credit risk are illustrated.After some conceptual background material, a journey is taken through theregulatory aspects of CVA. The three most commonly used methods for calculatingthe regulatory CVA capital charge are explained in detail and potentialchallenges with the methods are addressed. Further, the document analyses ingreater depth two of the methods; the internal model method (IMM) and thecurrent exposure method (CEM). The differences between these two methods areexplained mathematically and analysed. This comparison is supported bysimulations of portfolios containing interest rate swap contracts with differenttime to maturity and of counterparties with varying credit ratings. Oneconcluding observations is that credit valuation adjustment is a measure of centralimportance within counterparty credit risk. Further, it is shown that IMM has someimportant advantages over CEM, especially when it comes to model connection withreality. Finally, some possible future work to be done within the topic area is suggested.

Before the global financial crisis around 2008, the priority of the credit margin was comparatively low and was not taken into consideration as much as today. Many actors believed that credit risk could be neglected at various valuations. Due to that a lot of parties went bankrupt because of the low priorities. Today, this is a natural component in the financial market due to the capital regulation CRR and the Capital requirement directives (CRD IV), which are directly related to Basel III. In this thesis the authors have created a Credit valuation adjustment model, or a CVA-model, on behalf of the consulting firm AGL who want to use it in negotiations of interest rate swap with financial institutions. Factors as expected exposure, loss given default and probability of default are estimated in order to estimate a fair value for CVA. As a final product, the authors have created a model in VBA that can price CVA for individual contracts. This model is then evaluated and a sensitivity analysis is performed to see what impact credit rating and maturity have on the result.

Since the default of Lehman Brothers in 2008, it has become increasingly important to measure, manage and price the default risk in financial derivatives. Default risk in financial derivatives is referred to as counterparty credit risk (CCR). The price of CCR is captured in Credit Valuation Adjustment (CVA). This adjustment should in principle always enter the valuation of a derivative traded over-the-counter (OTC). To calculate CVA, one needs to know the probability of default of the counterparty. Since CVA is a price, what one needs is the risk-neutral probability of default. The typical way of obtaining risk-neutral default probabilities is to build credit curves calibrated using Credit Default Swaps (CDS). However, for a majority of a bank's counterparties there are no CDSs liquidly traded. This constitutes a major challenge. How does one model the risk-neutral default probability in the absence of observable CDS spreads? A number of methods for constructing proxy credit curves have been proposed previously. A particularly popular choice is the so-called Nomura (or cross-section) model. In studying this model, we find some weaknesses, which in some instances lead to degenerate proxy credit curves. In this thesis we propose an altered model, where the modelling quantity is changed from the CDS spread to the hazard rate. This ensures that the obtained proxy curves are valid by construction. We find that in practice, the Nomura model in many cases gives degenerate proxy credit curves. We find no such issues for the altered model. In some cases, we see that the differences between the models are minor. The conclusion is that the altered model is a better choice since it is theoretically sound and robust.
Sedan Lehman Brothers konkurs 2008 har det blivit allt viktigare att mäta, hantera och prissätta kreditrisken i finansiella derivat. Kreditrisk i finansiella derivat benämns ofta motpartsrisk (CCR). Priset på motpartsrisk fångas i kreditvärderingsjustering (CVA). Denna justering bör i princip alltid ingå i värderingen av ett derivat som handlas över disk (eng. over-the-counter, OTC). För att beräkna CVA behöver man veta sannolikheten för fallissemang (konkurs) hos motparten. Eftersom CVA är ett pris, behöver man den riskneutrala sannolikheten för fallissemang. Det typiska tillvägagångsättet för att erhålla riskneutrala sannolikheter är att bygga kreditkurvor kalibrerade med hjälp av kreditswappar (CDS:er). För en majoritet av en banks motparter finns emellertid ingen likvid handel i CDS:er. Detta utgör en stor utmaning. Hur ska man modellera riskneutrala fallissemangssannolikheter vid avsaknad av observerbara CDS-spreadar? Ett antal metoder för att konstruera proxykreditkurvor har föreslagits tidigare. Ett särskilt populärt val är den så kallade Nomura- (eller cross-section) modellen. När vi studerar denna modell hittar vi ett par svagheter, som i vissa fall leder till degenererade proxykreditkurvor. I den här uppsatsen föreslår vi en förändrad modell, där den modellerade kvantiteten byts från CDS-spreaden till riskfrekvensen (eng. hazard rate). Därmed säkerställs att de erhållna proxykurvorna är giltiga, per konstruktion. Vi finner att Nomura-modellen i praktiken i många fall ger degenererade proxykreditkurvor. Vi finner inga sådana problem för den förändrade modellen. I andra fall ser vi att skillnaderna mellan modellerna är små. Slutsatsen är att den förändrade modellen är ett bättre val eftersom den är teoretiskt sund och robust.

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Apesar das recentes turbulências nos mercados, a utilização de derivativos negociados fora de uma câmara de compensação tem apresentado rápido crescimento, constituindo um dos maiores componentes do mercado financeiro global. A correta inclusão da estrutura de dependência entre fatores de crédito e mercado é de suma importância no apreçamento do risco de crédito adjacente a exposições geradas por derivativos. Este é o apreçamento, envolvendo simulações de Monte Carlo, feito por uma instituição negociante para determinar a redução no valor do seu portfólio de derivativos devido a possibilidade de falência da contraparte. Este trabalho apresenta um modelo com abordagem paramétrica para lidar com a estrutura de dependência, intuitivo e de fácil implementação. Ao mesmo tempo, os números são contrastados com os resultados obtidos através de uma abordagem neutra ao risco para um portfólio replicante, sob o mesmo processo estocástico. O modelo é aplicado sobre um contrato a termo de câmbio, e diferentes cópulas e fatores de correlação são utilizados no processo estocástico.
Despite recent turmoils, the use of derivatives traded outside of a clearinghouse has shown rapid growth and is a major component of the global financial market. The correct inclusion of the dependence structure between market and credit factors is of high importance in the pricing of credit risk exposures generated by the adjacent derivatives. This pricing, involving Monte Carlo simulations, is done by a dealer to determine the reduction in the value of its derivatives portfolio because of the bankruptcy of the counterparty. This paper presents a model with parametric approach to deal with the dependence structure, intuitive and easily implemented. Meanwhile, the numbers are contrasted with results obtained using a risk neutral approach for a replicating portfolio under the same stochastic process. The model is applied on a forward exchange contract, and different copulas and correlation factors are used in the stochastic process.

Nous entamons ce rapport de thèse par l’évaluation de l’espérance espérée qui représente une des composantes majeures des ajustements XVA. Sous l’hypothèse d’indépendance entre l’exposition et les coûts de financement et de crédit, nous dérivons dans le chapitre 3 une représentation nouvelle de l’exposition espérée comme la solution d’une équation différentielle ordinaire par rapport au temps d’observation du défaut. Nous nous basons, pour le cas unidimensionnel, sur des arguments similaires à ceux de la volatilité locale de Dupire. Et pour le cas multidimensionnel, nous nous référons à la formule de la Co-aire. Cette représentation permet d’expliciter l’impact de la volatilité sur l’exposition espérée : Cette valeur temps fait intervenir la volatilité des sous-jacents ainsi que la sensibilité au premier ordre du prix, évalués sur un ensemble fini de points. Malgré des limitations numériques, cette méthode est une approche précise et rapide pour la valorisation de la XVA unitaire en dimension 1 et 2.Les chapitres suivants sont dédiés aux aspects du risque de corrélations entre les enveloppes d’expositions et les coûts XVA. Nous présentons une modélisation du risque général de corrélation à travers une diffusion stochastique multivariée, comprenant à la fois les sous-jacents des dérivés et les intensités de défaut. Dans ce cadre, nous exposons une nouvelle approche de valorisation par développements asymptotiques, telle que le prix d’un ajustement XVA correspond au prix de l’ajustement à corrélation nulle, auquel s’ajoute une somme explicite de termes correctifs. Le chapitre 4 est consacré à la dérivation technique et à l’étude de l’erreur numérique dans le cadre de la valorisation de dérivés contingents au défaut. La qualité des approximations numériques dépend uniquement de la régularité du processus de diffusion de l’intensité de crédit, et elle est indépendante de la régularité de la fonction payoff. Les formules de valorisation pour CVA et FVA sont présentées dans le chapitre 5. Une généralisation des développements asymptotiques pour le cadre bilatéral de défaut est adressée dans le chapitre 6.Nous terminons ce mémoire en abordant un cas du risque spécifique de corrélation lié aux contrats de migration de rating. Au-delà des formules de valorisation, notre contribution consiste à présenter une approche robuste pour la construction et la calibration d’un modèle de transition de ratings consistant avec les probabilités de défaut implicites de marché
The point of departure of this thesis is the valuation of the expected exposure which represents one of the major components of XVA adjustments. Under independence assumptions with credit and funding costs, we derive in Chapter 3 a new representation of the expected exposure as the solution of an ordinary differential equation w.r.t the default time variable. We rely on PDE arguments in the spirit of Dupire’s local volatility equation for the one dimensional problem. The multidimensional extension is addressed using the co-area formula. This forward representation gives an explicit expression of the exposure’s time value, involving the local volatility of the underlying diffusion process and the first order Greek delta, both evaluated only on finite set of points. From a numerical perspective, dimensionality is the main limitation of this approach. Though, we highlight high accuracy and time efficiency for standalone calculations in dimensions 1 and 2.The remaining chapters are dedicated to aspects of the correlation risk between the exposure and XVA costs. We start with the general correlation risk which is classically modeled in a joint diffusion process for market variables and the credit/funding spreads. We present a novel approach based on asymptotic expansions in a way that the price of an XVA adjustment with correlation risk is given by the classical correlation-free adjustment to which is added a sum of explicit correction terms depending on the exposure Greeks. Chapter 4 is consecrated to the technical derivation and error analysis of the expansion formulas in the context of pricing credit contingent derivatives. The accuracy of the valuation approach is independent of the smoothness of the payoff function, but it is related to the regularity of the credit intensity model. This finding is of special interest for pricing in a real financial context. Pricing formulas for CVA and FVA adjustments are derived in Chapter 5, along with numerical experiments. A generalization of the asymptotic expansions to a bilateral default risk setting is addressed in Chapter 6.Our thesis ends by tackling the problem of modeling the specific Right-Way Risk induced by rating trigger events within the collateral agreements. Our major contribution is the calibration of a rating transition model to market implied default probabilities

On définit le risque de contrepartie comme le risque de détérioration de la qualité de crédit entrainant une incapacité de la contrepartie à remplir ses obligations contractuelles. De nos jours, ce risque ne se limite plus aux entreprises, mais s'est également étendu aux banques et autres institutions financières. Par conséquent, toute entité participant aux marchés dérivés OTC est exposée à ce risque. La «Credit Value Adjustment» (CVA) est la valeur de marché du risque de contrepartie. En raison de sa complexité, la mise en œuvre de la CVA demeure l'un des plus grands défis auxquels les banques font face depuis la dernière crise. Pour la plupart d’entre elles, sa mise en production nécessite des changements majeurs de l’infrastructure actuelle. En outre, le régulateur, dont le but est de renforcer la stabilité des marchés financiers, s’est également intéressé à la CVA en introduisant une nouvelle charge en capital liée au risque de contrepartie. Les contributions de notre thèse à la littérature existante sur le sujet se trouvent essentiellement aux chapitres 2, 3 et 4 du manuscrit. Dans les chapitres 2 et 3, nous proposons deux méthodes innovatrices pour le calcul de la CVA. Le chapitre 4 est, quant à lui, entièrement dédié à l’étude de la charge en capital réglementaire sous la régulation FRTB-CVA
Counterparty risk is defined as the risk of credit worthiness deterioration, making the counterparty unable to meet its contractual obligations. Nowadays, this risk is no longer confined to corporate clients but has spread out to other banks and financial institutions. As a consequence, any firm participating in the over-the-counter (OTC) derivatives market is exposed to this risk. Credit Value Adjustment (CVA) is the market value of counterparty credit risk. Implementation of CVA still remains one of the biggest challenges banks face since the last financial crisis, due to its complexity and cost of implementation. For most banks, pricing the whole CVA book requires major changes on the infrastructure they currently have. Furthermore, regulatory responses to the last financial turmoil aimed at strengthening the financial system by introducing new capital requirements. The Basel III regulatory standard was developed in this respect, prescribing an additional capital charge to cover CVA losses.Our contributions to the relevant literature are chapters 2, 3 and 4. In chapters 2 and 3, we propose two innovative approaches to compute CVA that allow a huge reduction in computational costs. Chapter 4 is devoted to the study of the CVA capital charge under the new FRTB-CVA regulation

In the thesis we analyse changes in derivatives valuation after the financial crisis and their impact on behaviour of financial institutions. We focus mainly on the changes related to counterparty credit risk and valuation adjustments. We describe in economical terms the relationship between counterparty credit risk and traditional credit risk, we also introduce management and modelling of this risk. In second part of the study we analyse the regulatory framework, in particular new capital requirement and mandatory central clearing of OTC derivatives. We discuss inconsistencies between regulatory and internal approaches to the counterparty risk measurement and also significant systemic risk connected to central counterparties. Finally we investigate the impact of changes in derivatives valuation on banks in both the EU and the Czech Republic. Specifically we are interested in optimal approach to entering into derivative trade.

Mestrado em Matemática Financeira
O Acordo de Basileia III prevê, além do aumento da qualidade e do nível de requisitos de capital, a revisão de métricas com vista a melhorar o nível de exposição ao Risco de Crédito de Contraparte (RCC). O objetivo deste trabalho é desenvolver metodologias para mensurar a exposição esperada ao RCC de derivados negociados fora de bolsa (Over-The-Counter – OTC), que consistem em contratos ligados ao futuro valor, ou situação, dos instrumentos subjacentes aos quais se referem. Neste contexto, a inovação do novo Acordo refere-se à introdução de um encargo de capital para cobrir o risco de perdas do valor de mercado do RCC esperado para os instrumentos derivados OTC. Estas potenciais perdas são denominadas Ajustamentos de Avaliação de Crédito (Credit Valuation Adjustment – CVA) e podem ser calculadas por diferentes métodos, dependendo para tal da aprovação do Banco de Portugal. Nas ilustrações, recorre-se frequentemente a Interest Rate Swaps, por serem o instrumento financeiro mais transacionado.
Basel III provides an increase of the quality and level of capital requirements, and also it presents a review of the metrics in order to improve the level of exposure to the Counterparty Credit Risk (CCR). In this framework I will develop methodologies to measure the expected exposure to the CCR of Over-the-Counter derivatives, which are contracts that are linked to the future value of the underlying instruments or situation to which they refer. In this context, Basel III innovation reports to the introduction of a capital charge to cover the risk of loss of the CCR Mark-to-Market expected value for OTC derivatives. These potential losses are called Credit Valuation Adjustments (CVA) and may be calculated using different methods, which must be approved by Banco de Portugal. There is a recurrent use of Interest Rate Swaps when providing examples, given that they are the most traded financial instruments.

L'objectif de cette thèse est de fournir à la banque Audi un outil à jour sur les façons de calculer le capital requis par Bâle pour certains risques financiers présents dans le portefeuille de la banque. La régulation internationale est en développement continu : des nouvelles approches sont proposées afin de couvrir au mieux les risques du marché et du secteur bancaire. Les crises financières récentes étaient à la base de ces réformes. De plus, la Banque Audi opère sur des marchés qui présentent des caractères spécifiques qu'il faut prendre en considération lors du calcul du capital requis. Cette thèse se concentre sur le risque de taux d'intérêt dans le livre de négociation de la banque, le risque de contrepartie et précisément l'ajustement d'évaluation de crédit tout en incorporant l'impact de la corrélation entre la qualité du crédit de la contrepartie et l'exposition prévue envers cette même contrepartie. La première partie de cette thèse traite de la nouvelle méthodologie suggérée par Bâle sur le Trading Book : Fundamental Review of the Trading Book. Le risque de taux d'intérêt est particulièrement analysé en utilisant la méthode standard, Sensitivity Based Approach (SBA), et des méthodes plus 'traditionnelles' de valeur à risque tout en utilisant différents modèles tels que Generalized Auto Regressive Conditional Heteroscedasticity (GARCH), l'Analyse en Composantes Principales (ACP), l'Analyse en composantes indépendantes (ACI) et la version dynamique du modèle de taux de Nelson Siegel (DNS). Une application sur des portefeuilles d'obligations zéro coupons de différentes devises permet d'identifier la diversification des résultats entre les marchés stables européens (comme la France), moins stables (exemple Etats-Unis) et les marchés émergents (tel la Turquie). La deuxième partie est consacrée au risque de Contrepartie. Récemment, un nouveau capital est requis par les normes de Bâle afin de couvrir ce genre de risque. En 2014, la méthode est publiée : Standardized Approach for Counterparty Credit Risk (SA-CCR). On applique cette méthode sur différents types de produits dérivés afin de comparer le capital demandé par cette approche à celui obtenu par les modèles internes. Les modèles internes incorporent les estimations historiques ainsi que les projections futures du marché tout en se basant sur des modèles bien connus tels que Vasicek et GARCH. Plusieurs structures de hedging sont mises en place afin de mesurer l'impact de chacune sur les deux montants de capitaux requis (sous la méthode standard ou l'IMM). L'effet sur des produits en EUR et USD reflété que le modèle interne demande 80% du capital standard quand aucune stratégie de hedging n'est mise en place. Par contre, le hedging semble être beaucoup plus favorisé par le modèle standard que le modèle interne. La troisième partie est toujours sur le risque de Contrepartie, mais se focalise sur l'ajustement d'´évaluation de crédit (CVA). Ce sujet ne faisait pas partie des capitaux requis sauf récemment. A cause de son grand impact durant les récentes crises financières. Dès lors, si une opération avec des produits dérivés ne passe pas par une central clearing houses, un capital pour le CVA est requis. Dans ce travail, on détaille les méthodes acceptées par Bâle afin de calculer ces capitaux et on les compare entre elles. La comparaison se fait en se basant sur des portefeuilles de swap de taux d'intérêts avec, comme contreparties, différents pays d'Investment Grade. Cet article incorpore en plus l'impact de la corrélation entre la détérioration de la qualité de la contrepartie et l'augmentation de l'exposition prévue avec cette contrepartie connue sous le nom de WrongWay Risk : des modèles de correction d'erreurs (ECM) sont mis en place afin de déterminer ce lien. Les résultats permettent de montrer l'importance d'utiliser les CDS des contreparties et non de se limiter à leur note (Investment Grade ou pas)
This thesis aims at providing Bank Audi with an updated tool to understand and investigate in given risk types encountered in their portfolios and the way Basel suggests computing their capital charges. International regulator is constantly changing and modifying previously used approaches to enhance the reflection of the market and banking sector risks. The recent financial crisis played a major role in these reforms, in addition the situation of Bank Audi and the markets it is operating in, represent certain specifications that should be accounted for. The work handles interest rate risk in the trading book, Counterparty Credit Risk faced with derivatives along a closer look on the Credit Valuation Adjustment topic and the incorporation of Wrong Way Risk. The first part discusses the new Fundamental Review of the Trading Book: focusing on the general interest rate risk factor, the paper compared Basel’s Sensitivity Based Approach (SBA) capital charge to more traditional approaches of VaR using several models such as Generalized Auto Regressive Conditional Heteroscedasticity (GARCH), Principal Components Analysis (PCA), Independent Components Analysis (ICA) and Dynamic Nelson Siegel. Application on portfolios with zero coupon bonds of different sovereigns revealed the divergence in results between stable markets (such as France and Germany), less stable (such as the USA) and emergent markets (such as Turkey). The second part is dedicated to the Counterparty Credit Risk. A new capital charge methodology was proposed by Basel and set as a standard rule in 2014: the Standardized Approach for Counterparty Credit Risk (SA-CCR). Applying this approach on different derivatives portfolios, we compared it to internal models. The internal methodologies incorporated historical estimations and future projections based on Vasicek and GARCH models. Different hedging cases were investigated on EUR and USD portfolios. The impact of each hedging technique and the difference between IMM and the standardized methods were highlighted in this work: without hedging, the internal approach amends 80% of the standardized capital whereas, in general, the hedging is encouraged more under the standardized approach relatively to its capital reduction under the internal model. The third part remains a part of the Counterparty Credit Risk however, the main focus in this work is the Credit Valuation Adjustment. This topic was neglected in terms of capital charge earlier but due to its important impact is now incorporated as a capital charge amended when no central clearing is put in place when dealing with derivatives. We focus on the regulatory approaches of capital computation, comparing both accepted approaches based on portfolios of interest rate swaps held with investment grade sovereigns. An incorporation of the Wrong Way Risk is another addition in this work: using Error Correction Models we were able to reflect the impact of the correlation between the exposure and the credit quality of the investment grade sovereign we are dealing with. Based on such results, a suggestion of a re-calibrated standardized approach is in place to encourage the use of the CDS as an indicator of the credit quality of the counterparty and not its grade (investment or not) as followed by the new Basel regulations

The credit valuation adjustment (CVA) on an over-the-counter derivative transaction is the price of the risk associated with the potential default of the counterparties to the trade. This dissertation provides an introduction to the concept of CVA, beginning with the required backdrop of counterparty risk and the basics of default risk modelling. Right and wrong way risks are central themes of the dissertation. A model for the pricing of both the unilateral and the bilateral CVA on a credit default swap (CDS) is implemented. Each step of this process is explained thoroughly. Results are reported and discussed for a range of parameters. The trends observed in the CDS CVA numbers produced by the model are all justified and the right and wrong way nature of the exposures captured. In addition, the convergence and stability of the numerical schemes utilised are shown to be appropriate. A case study, in which the model is applied to a set of market scenarios, concludes the dissertation. Since the field is far from established, a number of areas are suggested for further research. Copyright
Dissertation (MSc)--University of Pretoria, 2012.
Mathematics and Applied Mathematics
unrestricted

Dissertation presented as partial requirement for obtaining the Master’s degree in Statistics and Information Management, with a specialization in Risk Analysis and Management
The recent publication of IFRS 9 facilitates the use of hedge accounting, although some challenges arise as well. Hedge effectiveness is to be more align with risk management meaning that hedge accounting ineffectiveness will now be only related to factors such as counterparty credit risk whenever uncollateralized derivatives are to be used as hedge instruments. This master thesis is concerned with what may go wrong in a designated hedging relationship due to CVA and DVS volatility. Using Monte Carlo simulations and regression analysis the probability of hedging ineffectiveness as a function of probability of default perceived implied volatility is to be modelled.
A recente publicação da IFRS 9 facilita o uso da contabilidade de cobertura, ainda que acrescente de igual modo alguns desafios. A contabilidade de cobertura passa a estar mais alinhada com a gestão de risco o que significa que a sua ineficácia passa a estar mais relacionada com fatores com risco de contraparte sempre que se usem derivados não coletaralizados como instrumentos de cobertura. Esta tese de mestrado foca-se no impacto da volatilidade do CVA/DVA na contabilidade de cobertura. Fazendo uso de simulações Montes Carlo e regressões estatísticas, procura-se modelizar a probabilidade de ineficácia das coberturas em função em da volatilidade das probabilidades de default.

Public-Private-Partnership (P3) is gaining momentum as the delivery method for the development of public infrastructure. These projects, however, are exposed to economic risks. If the private parties are not comfortable with the level of the risks, they would not participate in the project and, as a result, the infrastructure will most likely not be realized. As an incentive for participation in the P3 project, private parties are sometimes offered guarantees against unfavorable economic risks. Therefore, the valuation of these guarantees is essential for deciding whether or not to participate in the project. While previous works focused on the valuation of guarantees, the incorporation of credit risk in the value of the P3 projects and the guarantees has been neglected. The effect of credit risk can be taken into account by using the rigorous Credit Value Adjustment method (CVA). CVA is a computationally demanding method that the valuation methods currently in the literature are not capable of handling. This research offers a novel approach for the valuation of guarantees and P3 projects which is computationally superior to the existing methods. Because of this computational efficiency, CVA can be implemented to account for credit risk. For the development of this method, a continuous stochastic differential equation (SDE) is derived from the forecasted curve of an economic risk. Using the SDE, the partial differential equation (PDE) governing the value of the guarantees will be derived. Then, the PDE will be solved using Finite Difference Method (FDM). A new feature for this method is that it obtains exercise strategies for the Australian guarantees. The present work extends the literature by providing a valuation method for the cases that multiple risks affect P3 projects. It also presents an approach for the valuation of the Asian style guarantee, a contract which reimburses the private party based on the average of risk factor. Finally, a hypothetical case study illustrates the implementation of the FDM-based valuation method and CVA to obtain the value of the P3 project and the guarantees adjusted for the counterparty credit risk.

This thesis is intended to give an overview of Credit Valuation Adjustment (CVA) techniques and adjacent concepts. Firstly, the historical events that preceded the initiative to reform the Basel regulations and to introduce CVA are summarized. After some conceptual background material, a journey is taken through the pricing aspects of CVA. The unilateral CVA and Debt Valuation Adjustment (DVA) are derived in the case where one party engaging in a transaction is assumed to be defaultable, while bilateral CVA is derived in the case where both parties in a transaction are assumed to be defaultable. In this context, hedging aspects are also examined and risk-neutral pricing of CVA is discussed. There are several methods for pricing the CVA which will be explained in detail, and potential challenges with the methods will be also addressed. The document analyses in greater depth two of the methods: advanced and semi-analytical (swaption approach). The differences between these two methods are explained mathematically and analyzed. This comparison is supported by simulations of portfolios containing interest rate swaps contracts. In the second part the thesis, the relation between CVA from a regulatory perspective, i.e. driven by the CVA capital charge introduced in the third Basel accord, CVA from an accounting perspective, i.e. driven by IFRS, and CVA from a market perspective, i.e. as a potentially tradable asset, is discussed.
O objetivo desta dissertação é proporcionar uma visão mais abrangente da técnica de Credit Valuation Adjustment (CVA). A visão que se pretende transmitir vai desde a origem do tema às diferentes abordagens para a implementação do ajustamento, passando obrigatoriamente pela temática das diferentes regulamentações produzidas pelos organismos reguladores europeus. Depois de explicados alguns conceitos chave sobre o tema em apreço, o foco da dissertação será sobre os aspetos de pricing do CVA. O CVA e Debt Valuation Adjustment (DVA) unilateral são obtidos no caso em que é assumida que uma das partes envolvida numa transação pode entrar em default, e o CVA bilateral é adotado quando ambas as partes envolvidas na transação assumem que podem entrar em default. Neste contexto, aspetos de cobertura vão ser examinados e o risk-neutral pricing do CVA irá ser analisado. Esta dissertação analisa em detalhe dois métodos de apuramento de CVA - standard e semi-analítico (swaption approach). As diferenças de apuramento dos dois métodos vão ser explicadas e analisadas matematicamente. Esta comparação é suportada por simulações a uma operação de um contrato de swap de taxa de juro. A segunda parte desta dissertação visa explicar a relação entre a perspetiva de CVA regulatório, i.e. a necessidade de apuramento de CVA para requisitos de capital introduzida pelo acordo de Basileia, o CVA numa perspetiva contabilística, i.e. requisitado pela IFRS, e o CVA numa perspetiva de mercado, i.e. como um ativo que pode ser transacionado.

碩士
國立清華大學
計量財務金融學系
103
Counterparty credit risk is basically the credit risk between over-the-counter (OTC) derivatives counterparties. Given the huge size of global OTC derivatives markets, counterparty credit risk has always be important. However, for many years before the 2007 crisis, counterparty credit risk with high rated institutions, sovereigns and collateral posting counterparties were largely underestimated or even ignored. Unfortunately, the recent crises showed that these are often the entities that represent the greatest counterparty credit risk -- think about Lehman Brothers, AIG, Bear Sterns and Greece etc. Credit Value Adjustment (CVA) is a price of cost in counterparty credit risk. It has become increasingly important for banks engaged in OTC derivatives trading. Economically, since CVA quantifies counterparty credit risk as a single, measureable, P&L number, banks are motivated in calculating CVA in order to accurately measure and properly manage their counterparty credit risk assumed. From the regulatory point of view, a capital charge for banks against CVA variability under Basel III framework comes into effect since 2013. The banks with the approval of internal model method (IMM) approach for market risk management can calculate their economic capital requirement based on the value at risk (VaR) of CVA, which can be lower than the capital charge based on the standardized approach. In this thesis, I propose a method for CVA VaR calculation based on the Jump-diffusion CIR (JCIR) hazard rate model. It is in accordance with the Basel III framework and it performs better than the historical simulation method, which is usually set as the benchmark method.

碩士
東吳大學
財務工程與精算數學系
101
Counterparty credit risk (CCR) is a contract within the validity period counterparties fail to fulfill a contractual obligation may result in the risk of loss. Basel Committee on Banking Supervision in 2011 report that the 2008 financial tsunami, the about two-thirds of the loss was caused by the CCR,therefore CCR began to receive attention.Basel III will measure the CCR indicator called credit valuation adjustment (CVA). CVA calculation process needs to be calibrated counterparty default intensity. Obtained by the simulation method can default swap the CVA and value. Based on the same assumption, get the counterparty default intensity calibration approximate analytical solution, and the CIR interest rate model assumptions, by the simulation can be obtained default interest rate swap (IRS) of the CVA. Finally, compare the different intensity of counterparty default calibration method and the Basel III adopted default intensity calibration method CVA may breach the IRS for its Value.The results show that the proposed counterparty default intensity calibration of the approximate analytic solution, the resulting value of the IRS and its CVA calculation with accurate and fast characteristics.

碩士
國立東華大學
國際企業學系
101
The thesis aims to study how financial institutions develop their credit valuation decision-making under the New Basel Capital Accord, Basel III, which promulgates the new requirement of allocated to various risky assets The thesis uses a Real Option Analysis (ROA) of the Binomial Option Price Model to enhance the ability of financial institutions to make the valuation decision under the new standards of Basel III. In this thesis, in accordance with the optimal Regulatory Capital model, the model determines the expected minimum cost to determine the future of best decision-making of each year in sequence for the period covering 2013-2019 for the case where a financial institution reach the threshold limitation of the Basel III agreement in advance. In addition, this thesis applies the method of Decision tree analysis applies the method of Decision tree analysis (DTA) and the Binomial Option Price Model to analyze the credit value adjustment (CVA) in order to realize the credit value. Finally, the thesis makes comparisons between the different values of CVA to evaluate the optimal decision-making. This methodology can be used to help financial institutions realize their credit risk and minimize their losses in transitions.

碩士
東吳大學
財務工程與精算數學系
100
Under the report of Basel Committee on Banking Supervision in 2011,the counterparty credit risk (CCR) has been paid much attention because CCR resulted in roughly two-thirds of losses in financial crisis.In order to compensate for CCR,pricing for financial instruments is required to make adjustment to the net present value.The adjusted value is called credit valuation adjustment by Basel III.Recent literatures suggest that investor and counterparty may default,and therefore the bilateral counterparty credit risk (BCCR) is proposed. Under the base of BCCR,the adjustment to the net present value is called bilateral credit valuation adjustment (BCVA).Closeout is the net present value of the residual deal which is computed when one party defaults,and that is used for default settlement.A risk-free closeout is a net present value that assumes the surviving counterparty is default-free.International Swaps and Derivatives Association does not identify this assumption,thinking that real market can not ignore the survival of the party in the remaining duration,and suggests substitution closeout should be used.Brigo et al. (2011) proposed a simulate method to calculate BCVA for forward contract under the risk-free closeout and substitution closeout,and brought up the simplified formula for BCVA to explore the impact on forward contract with this simplified formula.In this article,the numerical solution of BCVA for the zero-coupon bond and forward contract under risk-free closeout,substitution closeout,and simplified formula is derived in order to increase the computing efficiency on real application.Furthermore,the numerical solution is utilized to investigate the impact of risk-free closeout,substitution closeout,and simplified formula on BCVA and pricing for zero-coupon bond and forward contract.

碩士
東吳大學
財務工程與精算數學系
100
Counterparty credit risk designates the risk of counterparty default and can not be paid in full payable amounts before the maturity of financial products, measured by credit valuation adjustment (CVA). If the investors and the counterparty are considered likely to default, it is known as bilateral counterparty credit risk, measured by bilateral credit valuation adjustment (BCVA). Wrong-way risk (WWR) and right-way risk (RWR) are to consider the correlation between the net present value of financial products with investor or counterparty default. Gregory (2010) merely considers the counterparty default with WWR and RWR, and derives the price of European option in numerical method. We assume that investors and counterparty will default with WWR and RWR, deriving the BCVA and price of European option in numerical method. Moreover, based on different situations, the impact of WWR and RWR on the price and BCVA of European option will be further discussed. The results demonstrated a greater impact from the counterparty's WWR or RWR on the BCVA and value of European option. Apart from that, the WWR from the counterparty indicated a greater impact than RWR from the counterparty. In addition, the impact of WWR and RWR on out of the money European option's BCVA and value is tremendous.

碩士
東吳大學
財務工程與精算數學系
102
The Basel III Accord will counterparty credit risk (CCR) to adjust the value called credit valuation adjustment (CVA). Recent literatures suggest that investor and counterparty may default, and therefore the bilateral counterparty credit risk (BCCR) is proposed. Under the base of BCCR, the adjustment to the net present value is called bilateral credit valuation adjustment (BCVA). This article consider a constant elasticity of variance (CEV) of the LM model which is proposed by Andersen and Andreasen (2000), and is called CEV-LM model. In this article, the value of the credit valuation adjustment for IRS with bilateral counterparty credit risk in the CEV-LM model. The situational analysis, default correlation, different contract maturities and the beginning of the volatility will affect bilateral credit valuation adjustment for interest rate swap. However, when the beginning of the volatility about the same, bilateral credit valuation adjustment for interest rate swap in different local volatility model is not affected.

碩士
東吳大學
財務工程與精算數學系
100
With the continuous development of financial markets, many financial institutions have complex transaction contract between each other, Lehman Brothers declared bankruptcy in 2008 and triggered a financial tsunami, led to many banks and insurance companies have been default, so supervisory agencies starting to focus on counterparty credit risk (CCR) control. The so-called CCR refers to the risk of default by the counterparty in the contract within the expiration date, credit valuation adjustment (CVA) is the measure of CCR. Calculate the CVA process requires an estimate of counterparty default time, recovery rate and the value of financial instruments. In this article, Andersen and Sidenius (2004) proposed the random recovery rate model that can assume recovery rate and default time with the correlation, we derived the closed-form solution of CVA for zero-coupon bond under the random recovery rate model. Finally, under the assumption of the CCR, discuss the correlation between recovery rate and the default to the impact of CVA. The results show that the greater the correlation coefficient, the recovery rate fluctuations the greater degree of CVA for zero-coupon bond. The greater the recovery rate volatility, the correlation coefficient fluctuations the greater degree of value for zero-coupon bond. If the real recovery rate is random Constant recovery rate will underestimate the zero-coupon bond, CVA, and overestimated the value of zero-coupon bond.

In this work we are introducing a risk neutral valuation formula for counterparty default risk adjustments in an unilateral and in a bilateral case. In the unilateral case the adjustment is represented by a Credit Valuation Adjust- ment(CVA) and in the bilateral case the adjustment is quantified by a Bilateral Risk Adjustment(BVA). We are incorporating these adjustments into the values of zero coupon bonds, coupon bearing bonds and interest rate swaps. For such an incorporation, risk neutral default probabilities extracted from the market quotes of Credit Default Swaps are needed. A Bootstrap method is used to derive them and a reduced form approach is used to model the default times. In the practical part, we are calculating Greek and Czech risk neutral default probabilities during the years 2008-2010. We are calculating CVA for 18 quoted Greek government bonds and we are comparing the adjusted prices with the market quoted prices of these bonds. We study the impact of a risk free interest rate curve choice on such a valuation. In the last sections, we construct an interest rate swap between the Czech and the Greece. We compute and study CVA and BVA for this interest rate swap.

Counterparty Credit Risk and Interest Rate Derivatives Pricing Jakub Černý Abstract: This thesis deals with the pricing of OTC financial derivatives including the coun- terparty credit risk (CCR). It focuses on the interest rate derivatives for which the interest rate must be modeled as random. This is where they differ from the pricing of other derivatives. The credit valuation adjustment (CVA) concept is used to calculate CCR which is in line with current banking regulation Basel III. When we assume the independence of the underlying asset and the credit quality of the counterparty, we obtain an analytical expression of CVA. However, if the independence is violated, the CVA calculation becomes quite complicated. Specifically, the CVA of the inter- est rate swap (IRS) is calculated mainly using the simulation approach which is time and computationally consuming. Therefore, we bring two new methods for IRS CVA calculation where the CVA is expressed in a semi-analytical form. These methods use copula functions, particularly the Gaussian copula and the upper Fréchet bound, and we compare them numerically with a complex simulation study. Furthermore, we pro- pose a method of calibration of the correlation coefficient and we determine the impact of changes in the intensity of default on the final CVA with four...