Credit value adjustment (CVA), as a quantified measure of counterparty credit risk for financial derivatives, is becoming an increasingly important concept for the financial industry. In this thesis, we evaluate CVA for an interest rate swap via a new structural default model. In our model, the asset value of a company is assumed to follow meromorphic Lévy processes with infinite jumps but finite variation. One important advantage of our model is that we are able to assume a random recovery rate which depends on default severity. Compared with the case with a fixed recovery rate, we show that the effect on CVA with a random recovery rate is significant. / May 2016

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.

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.

Yes / Following the global financial crisis, the measurement of counterparty credit risk has become an essential part of the Basel III accord with credit value adjustment being one of the most prominent components of this concept. In this study, we extend the Merton structural credit risk model for counterparty credit risk calculation in the context of calculating the credit value adjustment mainly by estimating the probability of default. We improve the Merton model in a variance-convoluted-gamma environment to include default dependence between counterparties through a linear factor decomposition framework. This allows one to tackle dependence through a systematic common component. Our set-up allows for easier, faster and more accurate fitting for the credit spread. Results confirm that use of the variance-gamma-convolution clearly solves the vanishing credit spread problem for short time-to-maturity or low leverage cases compared to a Brownian motion environment and its modifications. / Ahmet Sensoy gratefully acknowledges support from Turkish Academy of Sciences under its Outstanding Young Scientist Award Programme (TUBA-GEBIP). Frank J. Fabozzi acknowledges the financial support from EDHEC Business School.

The main target of this thesis is to summarize and explain the specifics of power markets and test application of models, which might be used especially in risk management area. Thesis starts with definition of market subjects, typology of traded contracts and description of market development with focus on Czech Republic. Thesis continues with development of theoretical concepts of short term/spot electricity markets and potential link between spot and forward electricity markets. After deriving of those microeconomic fundamental models we continue with stochastic models (Jump Diffusion Mean Reverting process and Extreme Value Theory) in order to depict patterns of spot and forward power contracts price volatility. Last chapter deals with credit risk specifics of power trading and develops model (using concept known as Credit Value Adjustment) to compare economic efficiency of OTC and exchange power trading. Developed and described models are tested on selected power markets, again with focus on Czech power market data set.

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

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.

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.

In this thesis, the pricing of counterparty credit risk on an OTC plain vanilla interest rate swap is investigated. Counterparty credit risk can be defined as the risk that a counterparty in a financial contract might not be able or willing to fulfil their obligations. This risk has to be taken into account in the valuation of an OTC derivative. The market price of the counterparty credit risk is known as the Credit Value Adjustment (CVA). In a bilateral contract, such as a swap, the party’s own creditworthiness also has to be taken into account, leading to another adjustment known as the Debit Value Adjustment (DVA). Since 2013, the international accounting standards (IFRS) states that these adjustments have to be done in order to reflect the fair value of an OTC derivative. A short background and the derivation of CVA and DVA is presented, including related topics like various risk mitigation techniques, hedging of CVA, regulations etc.. Four different pricing frameworks are compared, two more sophisticated frameworks and two approximative approaches. The most complex framework includes an interest rate model in form of the LIBOR Market Model and a credit model in form of the Cox-Ingersoll- Ross model. In this framework, the impact of dependencies between credit and market risk factors (leading to wrong-way/right-way risk) and the dependence between the default time of different parties are investigated. / I den här uppsatsen har prissättning av motpartsrisk för en OTC ränteswap undersökts. Motpartsrisk kan definieras som risken att en motpart i ett finansiellt kontrakt inte har möjlighet eller viljan att fullfölja sin del av kontraktet. Motpartsrisken måste tas med I värderingen av ett OTC-derivat. Marknadspriset på motpartrisken är känt som Credit Value Adjustment (CVA). I ett bilateralt kontrakt, t.ex. som en swap, måste även den egna kreditvärdighet tas med i värderingen, vilket leder till en justering som är känd som Debit Value Adjustment (DVA). Sedan 2013 skall, enligt den internationella redovisningsstandarden (IFRS), dessa prisjusteringar göras vid redovisningen av värdet för ett OTC derivat. En kort bakgrund samt härledningen av CVA och DVA ar presenterade tillsammans med relaterade ämnen. Fyra olika metoder för att beräkna CVA har jämförts, två mer sofistikerade metoder och två approximativa metoder. I den mest avancerade metoden används en räntemodell i form av LIBOR Market Model samt en kreditmodell i form av en Cox-Ingersoll-Ross modell. I den här metoden undersöks även påverkan av CVA då det existerar beroenden mellan marknads

Counterparty risk calculations have gained importance after the latest financial crisis. The bankruptcy of Lehman Brothers showed that even large financial institutiones face a risk of default. Hence, it is important to measure the risk of default for all the contracts written between financial institutions. Credit Value Adjustment, CVA, is an industry standard method for such calculations. Nevertheless, the implementation of this method is contract dependent and the necessary computer simulations can be very intensive. Monte Carlo simulations have for a long time been known as a precise but slow technique to evaluate the cash flows for contracts of all kinds. Measuring the exposure of a contract written on structured products might require half a day of calculations if the implementation is written without significant optimization. Several ideas have been presented by researchers and applied in the industry, the idea explored and implemented in this thesis was based on using Artificial Neural Networks in Python. This procedure require a decomposition of the Expected Exposure calculation within the CVA and generating a large data set using a standard Monte Carlo simulation. Three network architectures have been tested and the final performance was compared with using standard techniques for the very same calculation. The performance gain was significant, a portfolio of 100 counterparties with 10 contracts each would take 20 minutes of calculations in total when using the best performing architecture whereas a parallel C++ implementation of the standard method would require 2.6 days.