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

After the financial crisis of 2008 regulators found that the derivative market, where financial institutions traded OTC derivatives with each other, played a significantrole in triggering the crisis. This led to the emergence of Counterparty Credit Risk(CCR) which is used to measure the exposure banks have to their counterparties. In simple terms CCR is a mix of Market and Credit risk which defines the risk that your counter party will go into bankruptcy. CCR involves the risk factors used in market risk since all of the derivatives are based on underlying assets such as interest rate and currencies. The thesis will focus on how one can backtest individual risk factors driving the value of OTC derivatives. We will present different Monte Carlo simulation techniques that are being used to simulate and represent all possible future outcomes for the risk factors. In order to better understand the performance of a chosen model and how to adjust the calibration window for the ingoing parameters, two different approaches are presented,Quantitative Backtesting and Statistical Backtesting. As an extension to this, a portfolio of interest rate Swaps are backtested whose value are driven by the evolution of the underlying risk factors. The backtesting ofthe portfolio is done with netting. The time horizon for the backtesting procedureis 2010-2020 giving the user up to 261 independent observations with a forecast length of 14 days. Both of the backtesting methods provide the practitioner with a graphical results guiding the user to choose an appropriate model and calibration method for simulating the risk factors. We found that a combination of the two approaches provides the best result. Hence, no backtesting method is superior the other. Instead they complement each other and should be used simultaneously. Using the two backtesting methods one can find a model that perfectly fit the underlying distribution of risk factors, theoretically. However, one should be careful since there will always be uncertainty about the future and there is no guarantee that tomorrow will follow historical evolution exactly.

The aim of this thesis is to address the implications of Basel III regulation on counterparty credit risk. We analysed the development of OTC market, we addressed systemic risk and the way how central counterparties could mitigate or spread the contagion among banks. We used simulated data to develop a stress test model to find out the impact of counterparty credit risk on banks' capital requirements, in case the interest rate increased extensively. Six pos- sible scenarios of interest rate levels were developed with ascending order of the IR level. From these scenarios we computed the exposure levels and credit valuation adjustment (CVA) as the market value of counterparty credit risk. We came to the following conclusions: (1) Czech banks have enough capital to withstand any interest rate increase in any scenario. (2) Banks with high expo- sure to derivatives like Bank of America, Citibank and JP Morgan would face severe problems if the interest rate increased. (3) There is no direct correlation between credit valuation adjustment and interest rate, the CVA increases faster with the increase of the interest rate.

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.

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.

Made available in DSpace on 2016-03-15T19:26:13Z (GMT). No. of bitstreams: 1 Rodrigo Vogliotti.pdf: 868389 bytes, checksum: e1b90368c40778893d720b9e7a0fe869 (MD5) Previous issue date: 2012-08-17 / The difficulty in developing a statistical model that includes random variables and the need for intensive data processing capacity are the main challenges for the measurement of counterparty credit risk. The need to know the exposure value at the time of default (EAD) on a derivative instrument is a decisive factor for pricing, portfolio management and capital allocation. Recent events such as the creation of innovative products, coming from the new Basel Accord (Basel II) and the credit crisis of 2007/08 reinforce the importance of knowing what the actual credit risk exposure in a particular transaction. The aim of this study was to develop models for measuring credit risk of the counterparty from the estimation of counterparty exposure to bonds, equities and forward contract through the use of Monte Carlo simulation. The results of the sensitivity analysis indicate that certain parameters such as the interest rate, the mean and standard deviation show strong linear correlation with exposure (EAD) and this issue can be an important driver for the decision-making process. In the model of forward contract was found that correlated random variables can potentiate the exposure value. / A dificuldade em desenvolver um modelo estatístico que contemple variáveis aleatórias e a necessidade de intensa capacidade para processamento de dados são os principais desafios para a mensuração do risco de crédito de contraparte. A necessidade em conhecer o valor da exposição no momento do default (EAD) em um instrumento derivativo é fator decisivo para a precificação, gestão do portfólio e alocação de capital. Recentes acontecimentos como a criação de produtos inovadores, o advindo do novo acordo de Basileia (Basileia II) e a crise de crédito de 2007/08 reforçaram a importância de se saber qual o risco de crédito efetivo que cada contraparte está exposta em uma determinada transação. O objetivo deste estudo foi desenvolver modelos para mensuração do risco de crédito da contraparte a partir da estimação da exposição da contraparte para títulos, ações e contrato a termo de ações através da utilização da simulação de Monte Carlo. Os resultados da análise de sensibilidade indicam que certos parâmetros como a taxa de juro, a média e o desvio padrão apresentam forte correlação linear com a exposição (EAD) calculada e podem ser importantes direcionadores para o processo decisório. No modelo de contrato a termo de ações foi verificado que variáveis aleatórias correlacionadas potencializam o valor da exposição.

The paper is concerned with counterparty credit risk management for credit default swaps in the presence of default contagion. In particular, we study the impact of default contagion on credit value adjustments such as the BCCVA (Bilateral Collateralized Credit Value Adjustment) of Brigo et al. 2012 and on the performance of various collateralization strategies. We use the incomplete-information model of Frey and Schmidt (2012) as vehicle for our analysis. We find that taking contagion effects into account is important for the effectiveness of the strategy and we derive refined collateralization strategies to account for contagion effects. (authors' abstract) / Series: Research Report Series / Department of Statistics and Mathematics

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...