This study employs Extreme Value Theory and several univariate methods to compare their Value-at-Risk and Expected Shortfall predictive performance. We conduct several out-of-sample backtesting procedures, such as uncondi- tional coverage, independence and conditional coverage tests. The dataset in- cludes five different stock markets, PX50 (Prague, Czech Republic), BIST100 (Istanbul, Turkey), ATHEX (Athens, Greece), PSI20 (Lisbon, Portugal) and IBEX35 (Madrid, Spain). These markets have different financial histories and data span over twenty years. We analyze the global financial crisis period sep- arately to inspect the performance of these methods during the high volatility period. Our results support the most common findings that Extreme Value Theory is one of the most appropriate risk measurement tools. In addition, we find that GARCH family of methods, after accounting for asymmetry and fat tail phenomena, can be equally useful and sometimes even better than Extreme Value Theory based method in terms of risk estimation. Keywords Extreme Value Theory, Value-at-Risk, Expected Shortfall, Out-of-Sample Backtesting Author's e-mail ozturkdurmus@windowslive.com Supervisor's e-mail ies.avdulaj@gmail.com

The first part of this thesis studies tail probabilities forelliptical distributions and probabilities of extreme eventsfor multivariate stochastic processes. It is assumed that thetails of the probability distributions satisfy a regularvariation condition. This means, roughly speaking, that thereis a non-negligible probability for very large or extremeoutcomes to occur. Such models are useful in applicationsincluding insurance, finance and telecommunications networks.It is shown how regular variation of the marginals, or theincrements, of a stochastic process implies regular variationof functionals of the process. Moreover, the associated tailbehavior in terms of a limit measure is derived. The second part of the thesis studies problems related toparameter estimation in stochastic models with long memory.Emphasis is on the estimation of the drift parameter in somestochastic differential equations driven by the fractionalBrownian motion or more generally Volterra-type processes.Observing the process continuously, the maximum likelihoodestimator is derived using a Girsanov transformation. In thecase of discrete observations the study is carried out for theparticular case of the fractional Ornstein-Uhlenbeck process.For this model Whittle’s approach is applied to derive anestimator for all unknown parameters.

optimizationover a discrete number of random variables. In this paperwe extend this theory from the discrete to the continuous case, andconsider the limiting distribution of the location of the best offer asthe number of offers tends to infinity.Given a set   Rd of possible offers we seek a distribution over ,the argmax measure of the best offer. It depends on , the samplingdistribution of offer locations, and a measure index , which assignsto each point x 2  a probability distribution of offers.This problem is closely related to argmax theory of marked pointprocesses, altough we consider deterministic sequences of points inspace, to allow for greater generality. We first define a finite sampleargmax measure and then give conditions under which it converges asthe number of offers tends to infinity.To this end, we introduce a max-field of best offers and use continuityproperties of this field to calculate the argmax measure. Wedemonstrate the usefulness of the method by giving explicit formulasfor the limiting argmax distribution for a large class of models, includingexponential independent offers with a deterministic, additivedisturbance term. Finally, we illustrate the theory by simulations.

(None) Technical Summary of Thesis: The topic of my thesis is currency crisis. Currency crises have been a recurrent feature of the international economy from the invention of paper money. They are not confined to particular economies or specific region. They take place in developed, emerging, and developing countries and are spread all over the globe. Countries that experience currency crises face economic losses that can be huge and disruptive. However, the exacted toll is not only financial and economic, but also human, social, and political. It is clear that the currency crisis is a real threat to financial stability and economic prosperity. The main objective of this thesis is to analyze the determinants of currency crises for twenty OECD countries and South Africa from 1970 through 1998. It systematically examines the role of economic fundamentals and contagion in the origins of currency crises and empirically attempts to identify the channels through which the crises are being transmitted. It also examines the links between the incidence of currency crises and the choice of exchange rate regimes as well as the impact of capital market liberalization policies on the occurrence of currency crises. The first chapter identifies the episodes of currency crisis in our data set. Determining true crisis periods is a vital step in the empirical studies and has direct impact on the reliability of their estimations and the relevant policy implications. We define a period as a crisis episode when the Exchange Market Pressure (EMP) index, which consists of changes in exchange rates, reserves, and interest rates, exceeds a threshold. In order to minimize the concerns regarding the accuracy of identified crisis episodes, we apply extreme value theory, which is a more objective approach compared to other methods. In this chapter, we also select the reference country, which a country’s currency pressure index should be built around, in a more systematic way rather than by arbitrary choice or descriptive reasoning. The second chapter studies the probability of a currency exiting a tranquil state into a crisis state. There is an extensive literature on currency crises that empirically evaluate the roots and causes of the crises. Despite the interesting results of the current empirical literature, only very few of them account for the influence of time on the probability of crises. We use duration models that rigorously incorporate the time factor into the likelihood functions and allow us to investigate how the amount of time that a currency has already spent in the tranquil state affects the stability of a currency. Our findings show that high values of volatility of unemployment rates, inflation rates, contagion factors (which mostly work through trade channels), unemployment rates, real effective exchange rate, trade openness, and size of economy increases the hazard of a crisis. We make use of several robustness checks, including running our models on two different crisis episodes sets that are identified based on monthly and quarterly type spells. The third chapter examines the links between the incidence of currency crises and the choice of exchange rate regimes as well as the impact of capital market liberalization policies on the occurrence of currency crises. As in our previous paper, duration analysis is our methodology to study the probability of a currency crisis occurrence under different exchange rate regimes and capital mobility policies. The third chapter finds that there is a significant link between the choice of exchange rate regime and the incidence of currency crises in our sample. Nevertheless, the results are sensitive to the choice of the de facto exchange rate system. Moreover, in our sample, capital control policies appear to be helpful in preventing low duration currency crises. The results are robust to a wide variety of sample and models checks.

(None) Technical Summary of Thesis: The topic of my thesis is currency crisis. Currency crises have been a recurrent feature of the international economy from the invention of paper money. They are not confined to particular economies or specific region. They take place in developed, emerging, and developing countries and are spread all over the globe. Countries that experience currency crises face economic losses that can be huge and disruptive. However, the exacted toll is not only financial and economic, but also human, social, and political. It is clear that the currency crisis is a real threat to financial stability and economic prosperity. The main objective of this thesis is to analyze the determinants of currency crises for twenty OECD countries and South Africa from 1970 through 1998. It systematically examines the role of economic fundamentals and contagion in the origins of currency crises and empirically attempts to identify the channels through which the crises are being transmitted. It also examines the links between the incidence of currency crises and the choice of exchange rate regimes as well as the impact of capital market liberalization policies on the occurrence of currency crises. The first chapter identifies the episodes of currency crisis in our data set. Determining true crisis periods is a vital step in the empirical studies and has direct impact on the reliability of their estimations and the relevant policy implications. We define a period as a crisis episode when the Exchange Market Pressure (EMP) index, which consists of changes in exchange rates, reserves, and interest rates, exceeds a threshold. In order to minimize the concerns regarding the accuracy of identified crisis episodes, we apply extreme value theory, which is a more objective approach compared to other methods. In this chapter, we also select the reference country, which a country’s currency pressure index should be built around, in a more systematic way rather than by arbitrary choice or descriptive reasoning. The second chapter studies the probability of a currency exiting a tranquil state into a crisis state. There is an extensive literature on currency crises that empirically evaluate the roots and causes of the crises. Despite the interesting results of the current empirical literature, only very few of them account for the influence of time on the probability of crises. We use duration models that rigorously incorporate the time factor into the likelihood functions and allow us to investigate how the amount of time that a currency has already spent in the tranquil state affects the stability of a currency. Our findings show that high values of volatility of unemployment rates, inflation rates, contagion factors (which mostly work through trade channels), unemployment rates, real effective exchange rate, trade openness, and size of economy increases the hazard of a crisis. We make use of several robustness checks, including running our models on two different crisis episodes sets that are identified based on monthly and quarterly type spells. The third chapter examines the links between the incidence of currency crises and the choice of exchange rate regimes as well as the impact of capital market liberalization policies on the occurrence of currency crises. As in our previous paper, duration analysis is our methodology to study the probability of a currency crisis occurrence under different exchange rate regimes and capital mobility policies. The third chapter finds that there is a significant link between the choice of exchange rate regime and the incidence of currency crises in our sample. Nevertheless, the results are sensitive to the choice of the de facto exchange rate system. Moreover, in our sample, capital control policies appear to be helpful in preventing low duration currency crises. The results are robust to a wide variety of sample and models checks.

This dissertation investigates the implications of using the Advanced Measurement Approaches (AMA) as a method to assess operational risk capital charges for banks and insurance companies within Basel II paradigms and with regard to U.S. regulations. Operational risk has become recognized as a major risk class because of huge operational losses experienced by many financial firms over the last past decade. Unlike market risk, credit risk, and insurance risk, for which firms and scholars have designed efficient methodologies, there are few tools to help analyze and quantify operational risk. The new Basel Revised Framework for International Convergence of Capital Measurement and Capital Standards (Basel II) gives substantial flexibility to internationally active banks to set up their own risk assessment models in the context of the Advanced Measurement Approaches. The AMA developed in this thesis uses actuarial loss models complemented by the extreme value theory to determine the empirical probability distribution function of the overall capital charge in terms of various classes of copulas. Publicly available operational risk loss data set is used for the empirical exercise.

<p>The first part of this thesis studies tail probabilities forelliptical distributions and probabilities of extreme eventsfor multivariate stochastic processes. It is assumed that thetails of the probability distributions satisfy a regularvariation condition. This means, roughly speaking, that thereis a non-negligible probability for very large or extremeoutcomes to occur. Such models are useful in applicationsincluding insurance, finance and telecommunications networks.It is shown how regular variation of the marginals, or theincrements, of a stochastic process implies regular variationof functionals of the process. Moreover, the associated tailbehavior in terms of a limit measure is derived.</p><p>The second part of the thesis studies problems related toparameter estimation in stochastic models with long memory.Emphasis is on the estimation of the drift parameter in somestochastic differential equations driven by the fractionalBrownian motion or more generally Volterra-type processes.Observing the process continuously, the maximum likelihoodestimator is derived using a Girsanov transformation. In thecase of discrete observations the study is carried out for theparticular case of the fractional Ornstein-Uhlenbeck process.For this model Whittle’s approach is applied to derive anestimator for all unknown parameters.</p>

The contributions of this thesis have mainly a dual purpose: introducing several multivariate statistical methodologies where in the major of the cases only stationary of the random variables is assumed, and also highlight some of the applied problems in risk management where extreme value theory may play a role. Mostly every chapter is selfcontained, they have its own more detailed introduction and short conclusion. / Die Kontributionen von dieser Dissertation haben ein doppeltes Ziel: die Darstellung von vielen multivariaten statistischen Verfahren, wobei in der Mehrheit der Fälle nur Stationarität von den Zufallsvariablen angenommen wurde, und die Anwendungen in Risikomanagement in welchem Extremwerttheorie eine wichtige Rolle spielen könnte. Die Struktur der Arbeit ist eigenständig, mit einer detaillierten Einführung und kurzen Zusammenfassung in jedem Kapitel.

Deregulation of the energy market and surging trading activities have made the energy markets even more volatile in recent years. Under such circumstances, it becomes increasingly important to assess the probability of rare and extreme price movement in the risk management of energy futures. Similar to other financial time series, energy futures exhibit time varying volatility and fat tails. An appropriate risk measurement of energy futures should be able to capture these two features of the returns. In the first portion of this dissertation, we use the conditional Extreme Value Theory model to estimate Value-at-Risk (VaR) and Expected Shortfall (ES) for long and short trading positions in the energy markets. The statistical tests on the backtests show that this approach provides a significant improvement over the widely used Normal distribution based VaR and ES models. In the second portion of this dissertation, we extend our analysis from a single security to a portfolio of energy futures. In recent years, commodity futures have gained tremendous popularity as many investors believe they provide much needed diversification to their portfolios. In order to properly account for any diversification benefits, we employ a time-varying conditional bivariate copula approach to model the dependence structure between energy futures. In contrast to previous studies on the same subject, we introduce fundamental supply and demand factors into the copula models to study the dependence structure between energy futures. We find that energy futures are more likely to move together during down markets than up markets. In the third part of this dissertation, we extend our study of bivariate copula models to multivariate copula theory. We employ a pair-copula approach to estimate VaR and ES of a portfolio consisting of energy futures, the S&P 500 index and the US Dollar index. Our empirical results show that although the pair copula approach does not offer any added advantage in VaR and ES estimation over a long backtest horizon, it provides much more accurate estimates of risk during the period of high co-dependence among assets after the recent financial crisis.

(None) Technical Summary of Thesis: The topic of my thesis is currency crisis. Currency crises have been a recurrent feature of the international economy from the invention of paper money. They are not confined to particular economies or specific region. They take place in developed, emerging, and developing countries and are spread all over the globe. Countries that experience currency crises face economic losses that can be huge and disruptive. However, the exacted toll is not only financial and economic, but also human, social, and political. It is clear that the currency crisis is a real threat to financial stability and economic prosperity. The main objective of this thesis is to analyze the determinants of currency crises for twenty OECD countries and South Africa from 1970 through 1998. It systematically examines the role of economic fundamentals and contagion in the origins of currency crises and empirically attempts to identify the channels through which the crises are being transmitted. It also examines the links between the incidence of currency crises and the choice of exchange rate regimes as well as the impact of capital market liberalization policies on the occurrence of currency crises. The first chapter identifies the episodes of currency crisis in our data set. Determining true crisis periods is a vital step in the empirical studies and has direct impact on the reliability of their estimations and the relevant policy implications. We define a period as a crisis episode when the Exchange Market Pressure (EMP) index, which consists of changes in exchange rates, reserves, and interest rates, exceeds a threshold. In order to minimize the concerns regarding the accuracy of identified crisis episodes, we apply extreme value theory, which is a more objective approach compared to other methods. In this chapter, we also select the reference country, which a country’s currency pressure index should be built around, in a more systematic way rather than by arbitrary choice or descriptive reasoning. The second chapter studies the probability of a currency exiting a tranquil state into a crisis state. There is an extensive literature on currency crises that empirically evaluate the roots and causes of the crises. Despite the interesting results of the current empirical literature, only very few of them account for the influence of time on the probability of crises. We use duration models that rigorously incorporate the time factor into the likelihood functions and allow us to investigate how the amount of time that a currency has already spent in the tranquil state affects the stability of a currency. Our findings show that high values of volatility of unemployment rates, inflation rates, contagion factors (which mostly work through trade channels), unemployment rates, real effective exchange rate, trade openness, and size of economy increases the hazard of a crisis. We make use of several robustness checks, including running our models on two different crisis episodes sets that are identified based on monthly and quarterly type spells. The third chapter examines the links between the incidence of currency crises and the choice of exchange rate regimes as well as the impact of capital market liberalization policies on the occurrence of currency crises. As in our previous paper, duration analysis is our methodology to study the probability of a currency crisis occurrence under different exchange rate regimes and capital mobility policies. The third chapter finds that there is a significant link between the choice of exchange rate regime and the incidence of currency crises in our sample. Nevertheless, the results are sensitive to the choice of the de facto exchange rate system. Moreover, in our sample, capital control policies appear to be helpful in preventing low duration currency crises. The results are robust to a wide variety of sample and models checks.