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.

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

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.

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...

Submitted by Eitan Chernizon (eitan.chernizon@sgcib.com) on 2013-02-15T17:46:24Z No. of bitstreams: 1 MODELAGEM DA DEPENDÊNCIA ENTRE FATORES DE CRÉDITO E MERCADO.pdf: 1474762 bytes, checksum: 19b13b065762c89e556619042eaf016d (MD5) / Approved for entry into archive by Suzinei Teles Garcia Garcia (suzinei.garcia@fgv.br) on 2013-02-18T12:58:52Z (GMT) No. of bitstreams: 1 MODELAGEM DA DEPENDÊNCIA ENTRE FATORES DE CRÉDITO E MERCADO.pdf: 1474762 bytes, checksum: 19b13b065762c89e556619042eaf016d (MD5) / Made available in DSpace on 2013-02-18T13:20:44Z (GMT). No. of bitstreams: 1 MODELAGEM DA DEPENDÊNCIA ENTRE FATORES DE CRÉDITO E MERCADO.pdf: 1474762 bytes, checksum: 19b13b065762c89e556619042eaf016d (MD5) Previous issue date: 2013-02-01 / 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.

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.

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

Since the global financial crisis of 2008, regulatory bodies worldwide have implementedincreasingly stringent requirements for measuring and pricing default risk in financialderivatives. Counterparty Credit Risk (CCR) serves as the measure for default risk infinancial derivatives, and Credit Valuation Adjustment (CVA) is the pricing method used toincorporate this default risk into derivatives prices. To calculate the CVA, one needs the risk-neutral Probability of Default (PD) for the counterparty, which is the centre in this type ofderivative.The traditional method for calculating risk-neutral probabilities of default involves constructingcredit curves, calibrated using the credit derivative Credit Default Swap (CDS). However,liquidity issues in CDS trading present a major challenge, as the majority of counterpartieslack liquid CDS spreads. This poses the difficult question of how to model risk-neutral PDwithout liquid CDS spreads.The current method for generating proxy credit curves, introduced by the Japanese BankNomura in 2013, involves a cross-sectional linear regression model. Although this model issufficient in most cases, it often generates credit curves unsuitable for larger counterpartiesin more volatile times. In this thesis, we introduce two Long Short-Term Memory (LSTM)models trained on similar entities, which use CDS spreads as input. Our introduced modelsshow some improvement in generating proxy credit curves compared to the Nomura model,especially during times of higher volatility. While the result were more in line with the tradedCDS-market, there remains room for improvement in the model structure by using a moreextensive dataset. / Ända sedan 2008 års finanskris har styrande finansiella organ ökat kraven för mätning ochprissättning av konkursrisk inom derivat. Ett område av särskilt högt intresse för detta arbete ärmotpartskreditrisker (CCR). I detta är Kreditvärdesjustering (CVA) den huvudsakliga metodenför prissättning av konkursrisk inom finansiella derivat och för att kunna få fram ett värde avCVA behövs en risk-neutral konkurssannolikhet (PD).En av de traditionella metoderna för att räkna ut denna sannolikhet är genom att skapakreditkurvor som sedan är kalibrerade utifrån CDS:ar. Detta handlade derivat (CDS) finns baraför ett mindre antal företag över hela världen vilket gör att en majoritet av marknaden saknaren tillräckligt handlad CDS. Lösning på detta är att ta fram proxy CDS för ett motsvarande bolag.Idag görs detta framförallt med en tvärsnitts-regressionsmodell som introducerades 2013 avden japanska banken Nomura. Den skapar i många fall rimliga kurvor men ett problem den harär att den oftare gör proxyn lägre än vad den borde vara.I detta arbete introducerar vi istället en LSTM modell som tränas på liknande företag. Resultatetav detta är att vi får en bättre modell i många fall för att skapa en proxy kurva men som delvishar liknande brister som Nomura modellen. Men med fortsatta undersökningar inom områdetsamt med mer data kan detta skapa en mer exakt och säkrare proxy modell.

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.