The global over-the-counter derivatives market reached a staggering 14.5 trillion US dollars in gross market value at the end of December 2007. Although OTC derivatives are extremely useful and versatile in transferring risks, it appears to be a double-edged sword. For every derivative transaction concluded in the OTC market, there are two parties involved – each of which is exposed to the other defaulting on the agreed terms and conditions of the contract. Counterparty credit risk is defined as the loss that will be incurred in the event that a counterparty fails to honour its financial obligations. This dissertation provides an overview of counterparty credit risk measurement from a theoretical point of view and puts an emphasis on the demonstration of the current solutions used in practice to address this problem. The author applies a bottom up approach to the problem by defining counterparty credit risk exposure on a contract (single-trade) level and expands this definition on a step-by-step basis to incorporate portfolio effects, such as correlation among underlying market variables as well as credit risk mitigation techniques, such as netting and collateral agreements, in measuring counterparty credit risk exposure on a counterparty level. The author also discusses related concepts which impact counterparty credit risk such as wrong-way risk and proposes an enhancement to the framework introduced by Finger (2000) for incorporating wrong-way risk into existing measures of counterparty credit risk exposure. Finger‟s framework is enhanced by the introduction of a structural model approach which can be used in establishing a functional and intuitive relationship between the probability of default of the counterparty and the underlying market variable to the derivative contract under consideration. This approach is also applied to a typical South African situation through the use of Monte Carlo simulation. The topic of counterparty credit risk modelling is a very relevant topic in modern finance, especially since the advent of Basel 2 which this dissertation also touches on in terms of the applications of counterparty credit risk modelling and how this relates to the minimum regulatory capital requirements set by bank regulators. Copyright / Dissertation (MSc)--University of Pretoria, 2009. / Mathematics and Applied Mathematics / unrestricted

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

Counterparty credit risk is an important type of financial risk. The importance of proper counterparty risk management became most apparent in the wake of the 2008 series of failures of several large banks. Correlation of market factors is an important issue in the calculation of CVA. A notable case of correlation is wrong-way risk which occurs whenever the probability of default of the counterparty is positively correlated with exposure. The basic formulas for CVA and basic counterparty credit risk models do not account for wrong-way risk because its modeling is nontrivial. This thesis aims to answer how well can the impact of wrong-way risk on CVA be approximated with an add-on which only depends on correlation between the price of the underlying asset and the credit spread of the counterparty. The thesis is supplemented by a fully documented implementation of the model in the Mathematica software.

Usage of financial measurements that address the default probability of counterparties have been market practice for some time. Quantifying counterparty credit risk is usually done through the credit value adjustment which adjusts the value from a risk-free value to a risky value. When quantifying the credit value adjustment there is an important assumption that the financial exposure (value) and probability of counterparty default are independent variables. Wrong-way risk implies a relationship where exposure and probability of default are increasing together. It is an unfavourable relationship since as a party stands to gain more the probability of the counterparty not being able to pay also increase. When removing the independency assumption, the quantification of the credit value adjustment becomes more complex and there are several different methodologies with the aim to quantify CVA without the independency assumption. This paper analyses different methods of quantification and discusses different potential mitigators of wrong-way risk. But also, a case study searching for potential wrong-way exposures at a Swedish investment bank. The case study considers whether the exposures could potentially be influenced by wrong-way risk through stress tests on different value adjustments. The stress tests change the value adjustment and in turn imply wrong-way movements. At an investment bank that work towards minimizing risk it would be surprising to find large wrong-way risk exposures. But there are some interesting observations which could be deemed as wrong-way movements and would be interesting for the bank to investigate. Overall for the bank, wrong-way risk exposure cannot be claimed as significant. Conclusions involve modelling approach I deem the most useful in a perspective of calibration methodology, computer efficiency and deviation. Also, some suggestion of further development of this paper. / Under en tid har användning av finansiella mått som inkluderar motpartskreditrisk varit marknadsstandard. Kreditvärdesjustering används för att kvantifiera motpartskreditrisk och justerar värdet från ett riskfritt till ett värde som inkluderar motpartskreditrisk. När man justerar värdet används ett viktigt antagande som säger att den finansiella exponeringen (värdet) samt sannolikheten att motparten inte uppfyller sina förpliktelser är oberoende variabler. Felvägsrisk implicerar ett förhållande där exponeringen och sannolikheten att motparten inte kan uppfylla sina förpliktelser ökar tillsammans. Det är ett ofördelaktigt förhållande eftersom när en part kan tjäna mer ökar sannolikheten att motparten inte kan betala. När oberoende-antagandet tas bort blir kvantifieringen mer komplex, men det finns flera olika metoder som kvantifierar kreditvärdesjusteringen utan oberoende-antagandet. Denna uppsats analyserar olika kvantifieringsmetoder och diskuterar olika metoder för att minimera felvägsrisk. Uppsatsen innehåller även en fältstudie med syfte att hitta felvägsrisk bland exponeringarna hos en svensk investeringsbank. Fältstudien överväger huruvida exponeringarna eventuellt kan vara influerade av felvägsrisk genom att stressa olika mått för värdejustering. Stresstesterna påverkar värdejusteringen som i sin tur kan implicera felvägsrisk. Hos en svensk investeringsbank vars arbete involverar att minimera risk hade det varit förvånande att hitta stora exponeringar med felvägsrisk. Men det finns vissa observationer som tycks påvisa ofördelaktiga förhållanden som tyder på felvägsrisk. Dessa observationer skulle vara intressant för banken att se över utifrån den potentiella felvägsrisken. Överlag för banken kan jag inte påstå att exponeringen av felvägsrisk är signifikant. Slutsatserna involverar vilken modelleringsmetod som jag anser är mest användbar utifrån kalibrering, dataeffektivitet och potentiell avvikelse. Samt några förslag på vidare utveckling av denna rapport.

Submitted by Rodrigo Trintino Ibelli (rtrintino@gmail.com) on 2015-09-03T14:07:52Z No. of bitstreams: 1 Rodrigo Ibelli - Dissertação MPFE 2015.pdf: 3255284 bytes, checksum: 0de3609857bb415d5d0cbb497ca4bcc9 (MD5) / Rejected by Renata de Souza Nascimento (renata.souza@fgv.br), reason: Rodrigo, boa tarde Seu trabalho foi rejeitado por não estar de acordo com as normas da ABNT. Estaremos encaminhando por e-mail o que deverá ser alterado. Att on 2015-09-03T17:24:46Z (GMT) / Submitted by Rodrigo Trintino Ibelli (rtrintino@gmail.com) on 2015-09-04T12:56:55Z No. of bitstreams: 1 Dissertaçao Rodrigo Trintino - MPFE 2015.pdf: 3252833 bytes, checksum: f36bd64ae587c8593a352f10e413b4b9 (MD5) / Rejected by Renata de Souza Nascimento (renata.souza@fgv.br), reason: Encaminhado por e-mail. on 2015-09-04T13:40:06Z (GMT) / Submitted by Rodrigo Trintino Ibelli (rtrintino@gmail.com) on 2015-09-04T15:35:27Z No. of bitstreams: 1 Rodrigo Ibelli - Dissertaçao MPFE 2015.pdf: 3252967 bytes, checksum: 704103711c8bcb1cb74c851713c144b3 (MD5) / Approved for entry into archive by Renata de Souza Nascimento (renata.souza@fgv.br) on 2015-09-04T15:36:29Z (GMT) No. of bitstreams: 1 Rodrigo Ibelli - Dissertaçao MPFE 2015.pdf: 3252967 bytes, checksum: 704103711c8bcb1cb74c851713c144b3 (MD5) / Made available in DSpace on 2015-09-04T21:12:42Z (GMT). No. of bitstreams: 1 Rodrigo Ibelli - Dissertaçao MPFE 2015.pdf: 3252967 bytes, checksum: 704103711c8bcb1cb74c851713c144b3 (MD5) Previous issue date: 2015-08-12 / A stock swap transaction is an alternative way for a company who want to enter into a long position on its own stocks or who intend to set up a repurchase program without having to dispose of cash or contract a loan, or even hedging against increases on its stock prices. In this swap transaction the company receives the return on its own stock, whilst paying a fixed or floating interest rate. However, this kind of swap presents wrong-way risk, that is, a positive dependence between the underlying asset and the counterparty’s default probability, which must be considered by dealers when pricing this kind of swap contracts. In this work we propose a model for incorporating dependence between default probabilities and the counterparty’s exposure in the calculation of the CVA for these kind of swaps. We use a Cox process to model default times, given that the stochastic default intensity follows a CIR model, and assuming that the factor driving the underlying stock price and the factor driving the default intensity are jointly given by a bivariate standard Gaussian distribution. We analyze the impact on CVA of incorporating wrong-way risk in this kind of swap transaction with different counterparties, and for different maturities and dependence levels. / Uma forma interessante para uma companhia que pretende assumir uma posição comprada em suas próprias ações ou lançar futuramente um programa de recompra de ações, mas sem precisar dispor de caixa ou ter que contratar um empréstimo, ou então se protegendo de uma eventual alta no preço das ações, é através da contratação de um swap de ações. Neste swap, a companhia fica ativa na variação de sua própria ação enquanto paga uma taxa de juros pré ou pós-fixada. Contudo, este tipo de swap apresenta risco wrong-way, ou seja, existe uma dependência positiva entre a ação subjacente do swap e a probabilidade de default da companhia, o que precisa ser considerado por um banco ao precificar este tipo de swap. Neste trabalho propomos um modelo para incorporar a dependência entre probabilidades de default e a exposição à contraparte no cálculo do CVA para este tipo de swap. Utilizamos um processo de Cox para modelar o instante de ocorrência de default, dado que a intensidade estocástica de default segue um modelo do tipo CIR, e assumindo que o fator aleatório presente na ação subjacente e que o fator aleatório presente na intensidade de default são dados conjuntamente por uma distribuição normal padrão bivariada. Analisamos o impacto no CVA da incorporação do riscowrong-way para este tipo de swap com diferentes contrapartes, e para diferentes prazos de vencimento e níveis de correlação.

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.

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