Within Central Counterparty Clearing, the Clearing House collects Initial Margin from its Clearing Members. The Initial Margin can be calculated in many ways, one of which is by applying the commonly used risk measure Value-at-Risk. However, Value-at-Risk has one major flaw, namely its inability to encapsulate Tail Risk. Due to this, there has for long been a desire to replace Value-at-Risk with Expected Shortfall, another risk measure that has shown to be much better suited to encapsulate Tail Risk. That said, Value-at-Risk is still used over Expected Shortfall, something which is mainly due to the fact that there is no consensus regarding how one should backtest Expected Shortfall. The goal of this thesis is to evaluate some of the most commonly proposed methods for backtesting Expected Shortfall. In doing this, several non-parametric backtests of Expected Shortfall are investigated using simulated data as well as market data from different types of securities. Moreover, this thesis aims to shed some light on the differences between Value-at-Risk and Expected Shortfall, highlighting why a change of risk measure is not as straightforward as one might believe. From the investigations of the thesis, several backtests are found to be sufficient for backtesting the Initial Margin with Expected Shortfall as the risk measure, the so called Minimally Biased Relative backtest showing the overall best performance of the looked at backtests. Further, the thesis visualizes how Value-at-Risk and Expected Shortfall are two risk measures that are inherently different in a real-world setting, emphasizing how one should be careful making conversions between the two based upon parametric assumptions.

The 2007 financial crisis highlighted the severe risks posed by counterparty defaults in financial markets. Assessing and addressing counterparty credit risk has consequently been a focal point of new regulations introduced in the wake of the crisis. The Central Clearing Counterparty (CCP) is at the heart of the solution, an entity dedicated to managing and mitigating counterparty risk in a market. CPPs manage risk by collecting collateral, referred to as margin, from the participants trading on the market. Appropriately sizing the margin is of utmost importance for the CCP to maintain the integrity of its operation and, by extension, protect the participants in the market. Most contemporary margin methodologies require significant resources which precludes frequent margin updates. In light of this issue, our work examines the capability of replicating the popular margin methodology Historical Simulation Value at Risk using machine-learning-based methods envisioning that an adequate such model could be used as a complement to the traditional model, providing real-time margin estimations. The experiment concerns portfolios containing stocks, bonds, and options and uses static market data and scenarios. We conclude that neither of the ensemble methods are sufficiently accurate, while both of the neural network-based models show moderate promise, warranting further development.

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.

This thesis introduces models for pricing credit default swaps (CDS) and evaluating the counterparty risk when buying a CDS in the over-the-counter (OTC) market from a counterpart subjected to default risk. Rather than assuming that the default of the referencing firm of the CDS is independent of the trading parties in the CDS, this thesis proposes models that capture the default correlation amongst the three parties involved in the trade, namely the referencing firm, the buyer and the seller. We investigate how the counterparty risk that CDS buyers face can be affected by default correlation and how their balance sheet could be influenced by the changes in counterparty risk. The correlation of corporate default events has been frequently observed in credit markets due to the close business relationships of certain firms in the economy. One of the many mathematical approaches to model that correlation is default contagion. We propose an innovative model of default contagion which provides more flexibility by allowing the affected firm to recover from a default contagion event. We give a detailed derivation of the partial differential equations (PDE) for valuing both the CDS and the credit value adjustment (CVA). Numerical techniques are exploited to solve these PDEs. We compare our model against other models from the literature when measuring the CVA of an OTC CDS when the default risk of the referencing firm and the CDS seller is correlated. Further, the model is extended to incorporate economy-wide events that will damage all firms' credit at the same time-this is another kind of default correlation. Advanced numerical techniques are proposed to solve the resulting partial-integro differential equations (PIDE). We focus on investigating the different role of default contagion and economy-wide events have in terms of shaping the default correlation and counterparty risk. We complete the study by extending the model to include bilateral counterparty risk, which considers the default of the buyer and the correlation among the three parties. Again, our extension leads to a higher-dimensional problem that we must tackle with hybrid numerical schemes. The CVA and debit value adjustment (DVA) are analysed in detail and we are able to value the profit and loss to the investor's balance sheet due to CVA and DVA profit and loss under different market circumstances including default contagion.

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.

The uppermost goal of this diploma thesis is aimed at identification and evaluation of the current trends in one of the largest segments of financial markets. Special attention has been devoted to the regulatory changes, which have not been completely implemented in all major jurisdictions so far. The introductory part deals with the nowadays situation and explanation of post-crisis measures leading to a higher level of transparency and system stability. The following chapters analyze the key elements contributing to specific trends whereby those findings are based on research studies published by the world leading universities and central banks. The author also observes alternative functional concepts in the market and potential impacts affecting real transactions. The final portion has been dedicated to analysis of practical implications in terms of increased costs related to the trades and possible prospective outlook of the OTC derivatives market. The whole text is accompanied by authors personal reflections and comparison between the most important trading regions in respect to the value of underlying assets.

By participating in the market a party buys and sells different types of contracts resulting in the collection of contracts growing. With a large collection of contracts come the hurdles of an increasing operational cost, a harder-to-manage order book, and an increase in counterparty risk. To combat these problems we set out to minimize the size and quantity of contracts by performing what is called a compression. We have looked into three different types of compression methods for interest rate swap contracts. One method is specialized for central clearing, Coupon Blending, and two methods for bilateral clearing, Closed Loops, and the Network Simplex Method. By using Monte Carlo Simulations, all three methods could be compared to one another to conclude the significant findings. The clear winner for centrally cleared contracts was Coupon Blending which could terminate over 92% of the contracts, and reduce the total absolute size of the contracts by over 75%. Network Simplex came in as a close second which could also reduce the total absolute size of the contracts by over 75% but only terminate 86%. Coupon Blending and Network Simplex, both had very similar accuracy in their compression. However, NetworkSimplex performed better at keeping the system’s total risk intact. For bilateral clearing, NetworkSimplex performed the best where the Closed Loops strategy was not an optimized approach. / Genom att delta i den finansiella marknaden köper och säljer en participant olika sorters kontrakt vilket resulterar i att samlingen av kontrakt växer. Med en ständigt växande samling av kontrakt skapas problem som, att kostnaden för hantering ökar, att orderbokens hantering blir svårare och en ökad risk för konkurs. För att undvika dessa problem kan man utföra kompression vilket är att försöka reducera kontrakten i antal och storlek. Vi har studerat tre olika typer av kompressionsstrategier för kompression av ränteswappar. Den första strategin är Coupon Blending som är specialiserad för central clearing medan de två andra, Closed Loops och Network Simplex Metoden är utvecklade för bilateral clearing. Genom att använda Monte Carlo Simuleringar på alla tre strategier kunde vi dra slutsatser kring deras egenskaper och effektivitet. Den bästa strategin var Coupon Blending som kunde terminera över 92% av alla kontrakt, och samtidigt reducera den totala absoluta storleken på kontrakten med 75%. Network Simplex presterade också bra och kunde reducera den totala absoluta storleken på kontrakten med 75% och terminera 86% av kontrakten. Coupon Blending och Network Simplex hade bägge en liknande noggrannhet, men Network Simplex var något bättre på att hålla systemets totala risk intakt. För bilateral clearing presterade Network Simplex bäst där Closed Loops strategin inte var tillräckligt optimerad.

Central Clearing Counterparties play a crucial role in financial markets, requiring robust risk management practices to ensure operational stability. A growing emphasis on risk analysis and stress testing from regulators has led to the need for sophisticated tools that can model extreme but plausible market scenarios. This thesis presents a method leveraging Wasserstein Generative Adversarial Networks with Gradient Penalty (WGAN-GP) to construct an independent scenario generator capable of modeling and generating return distributions for financial markets. The developed method utilizes two primary components: the WGAN-GP model and a novel scenario selection strategy. The WGAN-GP model approximates the multivariate return distribution of stocks, generating plausible return scenarios. The scenario selection strategy employs lower and upper bounds on Euclidean distance calculated from the return vector to identify, and select, extreme scenarios suitable for stress testing clearing members' portfolios. This approach enables the extraction of extreme yet plausible returns. This method was evaluated using 25 years of historical stock return data from the S&P 500. Results demonstrate that the WGAN-GP model effectively approximates the multivariate return distribution of several stocks, facilitating the generation of new plausible returns. However, the model requires extensive training to fully capture the tails of the distribution. The Euclidean distance-based scenario selection strategy shows promise in identifying extreme scenarios, with the generated scenarios demonstrating comparable portfolio impact to historical scenarios. These results suggest that the proposed method offers valuable tools for Central Clearing Counterparties to enhance their risk management. / Centrala motparter spelar en avgörande roll i dagens finansmarknad, vilket innebär att robusta riskhanteringsrutiner är nödvändiga för att säkerställa operativ stabilitet. Ökande regulatoriskt tryck för riskanalys och stresstestning från tillsynsmyndigheter har lett till behovet av avancerade verktyg som kan modellera extrema men troliga marknadsscenarier. I denna uppsats presenteras en metod som använder Wasserstein Generative Adversarial Networks med Gradient Penalty (WGAN-GP) för att skapa en oberoende scenariogenerator som kan modellera och generera avkastningsfördelningar för finansmarknader. Den framtagna metoden består av två huvudkomponenter: WGAN-GP-modellen och en scenariourvalstrategi. WGAN-GP-modellen approximerar den multivariata avkastningsfördelningen för aktier och genererar möjliga avkastningsscenarier. Urvalsstrategin för scenarier använder nedre och övre gränser för euklidiskt avstånd, beräknat från avkastningsvektorn, för att identifiera och välja extrema scenarier som kan användas för att stresstesta clearingmedlemmars portföljer. Denna strategi gör det möjligt att erhålla nya extrema men troliga avkastningar. Metoden utvärderas med 25 års historisk aktieavkastningsdata från S&P 500. Resultaten visar att WGAN-GP-modellen effektivt kan approximera den multivariata avkastningsfördelningen för flera aktier och därmed generera nya möjliga avkastningar. Modellen kan dock kräva en omfattande mängd träningscykler (epochs) för att fullt ut fånga fördelningens svansar. Scenariurvalet baserat på euklidiskt avstånd visade lovande resultat som ett urvalskriterium för extrema scenarier. De genererade scenarierna visar en jämförbar påverkan på portföljer i förhållande till de historiska scenarierna. Dessa resultat tyder på att den föreslagna metoden kan erbjuda värdefulla verktyg för centrala motparter att förbättra sin riskhantering.

Counterparty credit risk is present in trades offinancial obligations. This master thesis investigates the up and comingtechnology blockchain and how it could be used to mitigate counterparty creditrisk. The study intends to cover essentials of the mathematical model expectedloss, along with an introduction to the blockchain technology. After modellinga simple smart contract and using historical financial data, it was evidentthat there is a possible opportunity to reduce counterparty credit risk withthe use of blockchain. From the market study of this thesis, it is obvious thatthe current financial market needs more education about blockchain technology. / Motpartsrisk är närvarande i finansiella obligationer. Den här uppsatsen un- dersöker den lovande teknologin blockkedjan och hur den kan användas för att reducera motpartsrisk. Studien har för avsikt att täcka det essentiel- la i den matematiska modellen för förväntad förlust, samt en introduktion om blockkedjeteknologi. Efter att ha modellerat ett enkelt smart kontrakt, där historiska finansiella data använts, var det tydligt att det kan finnas en möjlighet att reducera motpartsrisk med hjälp av blockkedjan. Från mark- nadsundersökningen gjord i studien var det uppenbart att den nuvarande finansiella marknaden är i stort behov av mer utbildning om blockkedjan.

This thesis provides an end-to-end picture of the modelling of interest rates and Foreign Exchange (FX) rates. We start by defining the FX rates and the interest rates. After having a good understanding of the basics, we take a deep dive into the approaches commonly used to model interest rates and FX rates respectively. In particular, we present an interest rate model and a FX rate model that I have developed for man- aging Swedbank’s Counterparty Credit Risk (CCR). In addition to the mathematical derivations, we describe the theories underlying the models, discuss the model com- parisons, and explain the model choices made in practical applications. Finally, we provide a prototype of model implementation to illustrate how theory can be put into practice. I had some doubts about the interest rate model and the FX rate model that I have developed for managing Swedbank’s CCR. These doubts have been cleared up through this thesis work. Both the doubts and the clarifications are described in this thesis. / Denna uppsats tillför en helhetsbild av modellering av räntorna och valutakurserna. Vi börjar med att definiera räntorna och valutakurserna. Med en bra uppfattning av grunden, gör vi en djupdykning i de metoder som används för att modellera räntorna och valutakurserna respektive. I synnerhet presenterar vi en räntemodell och en valu- takursmodell, som jag har utvecklat för att hantera Swedbanks motpartsrisk. Förutom de matematiska härledningarna beskriver vi också modellernas underliggande teorier, diskuterar modellerjämförelser, och förtydligar de modellval som gjorts i praktiska tillämpningar. Slutligen använder vi en prototyp för att belysa genomförandet av modellerna. Jag var en smula tveksam till de riskfaktormodeller som jag har utvecklat för att hantera Swedbanks motpartsrisk. Jag har klargjort dessa tvivel genom att arbeta med den här uppsatsen. Både tvivlen och klargörandena beskrivs i denna rapport.