The aim of this master thesis is analyze the impact of new regulatory requirements for market risk in terms of internal approach of the selected portfolio. The first part deals with the definition and calculation methods of risk measures Value at Risk and Expected Shortfall. Furthermore, this part is dedicated to model backtesting and determination of the stress period. The second part describes the development of Basel I-III regulatory requirements for market risk with a focus on internal approaches. The third part focuses on the calculation and subsequent analysis of current and new regulatory reguirements for market risk using the historical simulation method, variance and covariance method and Monte Carlo simulation.

Structured products are complex non-linear financial instruments that make it difficult to calculate their future risk and return. Two categories of structured products are Capital Protected and Participation notes, which are built by bonds and options. Since the structured products are non-linear, it is difficult to asses their long-term risk today. This study, conducted at Nordea Markets, focuses on the risk of structured products and how the risk and return in a portfolio changes when we include structured products into it. Nordea can only calculate the one-year risk with their current risk advisory tool, which makes long time predictions difficult. To solve this problem, we have simulated portfolios and structured products over a five-year time horizon with the Monte Carlo method. To investigate how the structured product allocations behave in different conditions, we have developed three test methods and a ranking program. The first test method measures how different underlying assets changes the risk and return in the portfolio allocations. The second test method varies the drift, volatility, and correlation for both the underlying asset and the portfolio to see how these parameters changes the risk and return. The third test method simulates a crisis market with high correlations and low drift. All these tests go through the ranking program, the most important part, where the different allocations are compared against the original portfolio to decide when the allocations perform better. The ranking is based on multiple risk measures, but the focus in this study is at using Expected Shortfall for risk while the expected return is used for ranking the return. We used five different reference portfolios and six different structured products with specific parameters in an example run where the ranking program and all three test methods are used. We found that the properties of the reference portfolio and the structured product’s underlying are significant and affect the performance the most. In the example run it was possible to find preferable cases for all structured products but some performed better than others. The test methods revealed many aspects of portfolio allocation with structured products, such as the decrease in portfolio risk for Capital Protected notes and increase in portfolio return for Participation notes. Our ranking program proved to be useful in the sense that it simplifies the result interpretations.

The main objective of this thesis is to investigate whether multivariate models using Highfrequency data provide significantly more accurate forecasts of Value at Risk and Expected Shortfall than multivariate models using only daily data. Our objective is very topical since the Basel Committee announced in 2013 that is going to change the risk measure used for calculation of capital requirement from Value at Risk to Expected Shortfall. The further improvement of accuracy of both risk measures can be also achieved by incorporation of high-frequency data that are rapidly more available due to significant technological progress. Therefore, we employed parsimonious Heterogeneous Autoregression and its asymmetric version that uses high-frequency data for the modeling of realized covariance matrix. The benchmark models are chosen well established DCC-GARCH and EWMA. The computation of Value at Risk (VaR) and Expected Shortfall (ES) is done through parametric, semi-parametric and Monte Carlo simulations. The loss distributions are represented by multivariate Gaussian, Student t, multivariate distributions simulated by Copula functions and multivariate filtered historical simulations. There are used univariate loss distributions: Generalized Pareto Distribution from EVT, empirical and standard parametric distributions. The main finding is that Heterogeneous Autoregression model using high-frequency data delivered superior or at least the same accuracy of forecasts of VaR to benchmark models based on daily data. Finally, the backtesting of ES remains still very challenging and applied Test I. and II. did not provide credible validation of the forecasts.

This thesis deals with methods of stochastic programming and their application in financial investment. Theoretical part is devoted to basic terms of mathematical optimization, stochastic programming and decision making under uncertainty. Furter, there are introduced basic principles of modern portfolio theory, substantial part is devoted to risk measurement techniques in the context of investment, mostly to the methods Value at Risk and Expected shortfall. Practical part aims to creation of optimization models with an emphasis to minimize investment risk. Created models deal with real data and they are solved in optimization software GAMS.

We consider tail empirical processes for long memory stochastic volatility models with heavy tails and leverage. We show a dichotomous behaviour for the tail empirical process with fixed levels, according to the interplay between the long memory parameter and the tail index; leverage does not play a role. On the other hand, the tail empirical process with random levels is not affected by either long memory or leverage. The tail empirical process with random levels is used to construct a family of estimators of the tail index, including the famous Hill estimator and harmonic moment estimators. The limiting behaviour of these estimators is not affected by either long memory or leverage. Furthermore, we consider estimators of risk measures such as Value-at-Risk and Expected Shortfall. In these cases, the limiting behaviour is affected by long memory, but it is not affected by leverage. The theoretical results are illustrated by simulation studies.

This thesis includes four essays on risk assessment with financial econometrics models. The first chapter provides Monte Carlo evidence on the efficiency gains obtained in GARCH-base estimations of VaR and ES by incorporating dependence information through copulas and subsequently using full maximum likelihood (FML) estimates. First, individual returns series are considered; in this case, the efficiency gain stems from exploiting the relationship with another returns series using a copula model. Second, portfolio returns series obtained as a linear combination of returns series related with a copula model, are considered; in this case, the efficiency gain stems from using FML estimates instead of two-stage maximum likelihood estimates. Our results show that, in these situations, using copula models and FML leads to a substantial reduction in the mean squared error of the VaR and ES estimates (around 50\% when there is a medium degree of dependence between returns) and a notable improvement in the performance of backtesting procedures. Then, chapter 2 analyzes the impact of the COVID-19 pandemic on the conditional variance of stock returns. In this work, we look at this effect from a global perspective, employing series of major stock market and sector indices. We use the Hansen’s Skewed-t distribution with EGARCH extended to control for sudden changes in volatility. We oversee the COVID-19 effect on the VaR. Our results show that there is a significant sudden shift up in the return distribution variance post the announcement of the pandemic, which must be explained properly to obtain reliable measures for financial risk management. In chapter 3, we assess VaR and ES estimates assuming different models for standardised returns such as Cornish-Fisher and Gram-Charlier polynomial expansions, and well-known parametric densities such as normal, skewed Student-t family of Zhu and Galbraith (2010), and Johnson. This paper aims to check whether models based on polynomial expansions outperform the parametric ones. We carry out the model performance comparison in two stages. First, a backtesting analysis for VaR and ES, and second, using the loss function approach. Our backtesting results in our empirical exercise suggest that all distributions, but the normal, perform quite well in VaR and ES estimations. Regarding the loss function analysis, we conclude that the Cornish-Fisher expansion usually outperforms the others in VaR estimation, but Johnson distribution is the one that provides the best ES estimates in most cases. Although the differences among all distributions (excluding the normal) are not great. Finally, chapter 4 assess whether accounting for asymmetry and tail-dependence in returns distributions may help to identify more profitable investment strategies in asset portfolios. Three copula models are used to parameterize the multivariate distribution of returns: Gaussian, C-Vine and R-Vine copulas. Using data from equities and ETFs from the US market, we find evidence that, for portfolios of 48 constituents or less, the R-Vine copula is able to produce more profitable portfolios with respect to both, the C-Vine and Gaussian copulas. However, for portfolios of 100 assets, performance of R- and C-Vine copulas is quite similar, being both better than the Gaussian copula.

Since the Basel Committee on Banking Supervision first suggested a transition to Expected Shortfall as the primary risk measure for financial institutions, the question on how to backtest it has been widely discussed. Still, there is a lack of studies that compare the different proposed backtesting methods. This thesis uses simulations and empirical data to evaluate the performance of non-parametric backtests under different circumstances. An important takeaway from the thesis is that the different backtests all use some kind of trade-off between measuring the number of Value at Risk exceedances and their magnitudes. The main finding of this thesis is a list, ranking the non-parametric backtests. This list can be used to choose backtesting method by cross-referencing to what is possible to implement given the estimation method that the financial institution uses. / Sedan Baselkommittén föreslog införandet av Expected Shortfall som primärt riskmått för finansiella institutioner, har det debatteras vilken backtesting metod som är bäst. Trots detta råder det brist på studier som utvärderar olika föreslagna backtest. I studien används simuleringar och historisk data för att utvärdera icke-parametriska backtests förmåga att under olika omständigheter upptäcka underskattad Expected Shortfall. En viktig iakttagelse är att alla de undersökta testen innebär ett avvägande i vilken utsträckning det skall detektera antalet och/eller storleken på Value at Risk överträdelserna. Studien resulterar i en prioriterad lista över vilka icke-parametriska backtest som är bäst. Denna lista kan sedan användas för att välja backtest utefter vad varje finansiell institution anser är möjligt givet dess estimeringsmetod.

Quantifier et mesurer le risque dans un environnement partiellement ou totalement incertain est probablement l'un des enjeux majeurs de la recherche appliquée en mathématiques financières. Cela concerne l'économie, la finance, mais d'autres domaines comme la santé via les assurances par exemple. L'une des difficultés fondamentales de ce processus de gestion des risques est de modéliser les actifs sous-jacents, puis d'approcher le risque à partir des observations ou des simulations. Comme dans ce domaine, l'aléa ou l'incertitude joue un rôle fondamental dans l'évolution des actifs, le recours aux processus stochastiques et aux méthodes statistiques devient crucial. Dans la pratique l'approche paramétrique est largement utilisée. Elle consiste à choisir le modèle dans une famille paramétrique, de quantifier le risque en fonction des paramètres, et d'estimer le risque en remplaçant les paramètres par leurs estimations. Cette approche présente un risque majeur, celui de mal spécifier le modèle, et donc de sous-estimer ou sur-estimer le risque. Partant de ce constat et dans une perspective de minimiser le risque de modèle, nous avons choisi d'aborder la question de la quantification du risque avec une approche non-paramétrique qui s'applique à des modèles aussi généraux que possible. Nous nous sommes concentrés sur deux mesures de risque largement utilisées dans la pratique et qui sont parfois imposées par les réglementations nationales ou internationales. Il s'agit de la Value at Risk (VaR) qui quantifie le niveau de perte maximum avec un niveau de confiance élevé (95% ou 99%). La seconde mesure est l'Expected Shortfall (ES) qui nous renseigne sur la perte moyenne au delà de la VaR.

In this paper dependence between credit default swap (CDS) values and stock price movements of the largest European banking groups is examined and effectiveness of the usage of CDS contracts as a tool to hedge exposure to the price movements of the underlying stock during the pre-crisis and crisis periods is assessed. The effectiveness is evaluated by comparing estimated Value-at-Risk (VaR) and Expected Shortfall (ES) risk measures of portfolios consisting of stocks and CDS vis-à-vis portfolios consisting of only stocks. CDS are valued using mark-to-market approach. Marginal distributions of CDS value changes and stock returns are estimated using Kernel density estimate from historical time-series data of daily stock returns and CDS value changes. Dependence between marginal distributions is estimated using Gaussian, Gumbel and Student‟s t copulas. Random portfolio values are simulated using Monte Carlo Simulation from estimated copulas parameters and marginal distributions for daily, quarterly and yearly time horizons. VaR and ES with 90%, 95% and 99% confidence level are estimated from the simulated portfolio return distribution. The results show that there is a significant negative dependence between CDS values and stock prices during financial crisis while dependence is weak in the pre-crisis period. The main finding of the paper is that CDS added into the portfolio of stocks significantly reduces VaR and ES of a portfolio during the period of financial crisis while they... [to full text] / Šiame darbe tikrinama didţiausių Europos bankų grupių kredito rizikos apsikeitimo sandorių (CDS) ir akcijų kainų priklausomybė bei vertinamas CDS efektyvumas, jei jais draudţiamasi nuo akcijų kainų svyravimų prieš kriziniu ir kriziniu laikotarpiu. Efektyvumas yra įvertinamas lyginant apskaičiuotas rizikos vertes (VaR) ir tikėtinus vertės trūkumus (ES) dviejų portfelių: akcijų portfelio bei akcijų ir CDS portfelio. CDS vertinti yra naudojamas pagal rinką vertinimo būdas (mark-to-market approach). CDS verčių pasikeitimo ir akcijų grąţos ribiniai pasiskirstymai yra įvertinami, naudojant Kernel įvertinimą (Kernel Estimator) iš istorinių akcijų grąţų ir CDS verčių pokyčių duomenų. Priklausomybė tarp ribinių pasiskirstymų yra įvertinama naudojant Gauso, Gumbelio ir Studento t kopulas (copulas). Atsitiktinės portfelių vertės yra susimuliuojamos naudojant Monte Carlo simuliaciją, pritaikant kopulų parametrus bei kintamųjų ribinius pasiskirstymus vienos dienos, ketvirčio bei metų periodams. VaR ir ES su 90%, 95% ir 99% pasitikėjimo intervalais yra skaičiuojami iš susimuliuotų portfelio grąţų pasiskirstymo. Gauti rezultatai rodo, kad tarp akcijų kainų ir CDS verčių yra stipri priklausomybė krizės laikotarpiu, tuo tarpu prieš kriziniu laikotarpiu priklausomybė yra silpna. Pagrindinė darbo išvada yra ta, jog CDS įtraukti į akcijų portfelį reikšmingai sumaţina portfelio VaR ir ES kriziniu laikotarpiu, tačiau nesumaţina prieš kriziniu laikotarpiu. Portfelio rizika gali būti sumaţinta, jei... [toliau žr. visą tekstą]

Cette thèse se concentre sur des mesures du risque financier et la modélisation de la volatilité. L’objectifgénéral est : (i) de proposer de nouvelles techniques pour mesurer à la fois le risque systémique et lerisque à haute fréquence, et (ii) d’appliquer et d’améliorer les outils économétriques de modélisation etde prévision de la volatilité. Ce travail comporte quatre chapitres (papiers de recherche).La première partie de la thèse traite des questions liées à la modélisation et la prévision des mesuresdu risque à haute fréquence et du risque systémique. Plus précisément, le deuxième chapitre proposeune nouvelle mesure du risque systémique utilisée pour identifier les institutions financières d’importancesystémique (SIFIs). Basée sur une approche spécifique, cette mesure originale permet de décomposer lerisque global du système financier tout en tenant compte des caractéristiques de l’entreprise. Le troisièmechapitre propose des mesures du risque de marché intra-journalier dans le contexte particulier des donnéesà haute fréquence irrégulièrement espacées dans le temps (tick-by-tick).La deuxième partie de la thèse est consacrée aux méthodes d’estimation et de prévision de la volatilitéincluant directement des données à haute fréquence ou des mesures réalisées de volatilité. Ainsi, dans lequatrième chapitre, nous cherchons à déterminer, dans le contexte des modèles de mélange des fréquencesd’échantillonnage (MIDAS), si des regresseurs à haute fréquence améliorent les prévisions de la volatilitéà basse fréquence. Une question liée est de savoir s’il existe une fréquence d’échantillonnage optimaleen termes de prévision, et non de mesure de la volatilité. Le cinquième chapitre propose une versionrobuste aux jumps du modèle Realized GARCH. L’application porte sur la crise / This thesis focuses on financial risk measures and volatility modeling. The broad goal of this dissertationis: (i) to propose new techniques to measure both systemic risk and high-frequency risk, and (ii) toapply and improve advanced econometric tools to model and forecast time-varying volatility. This workhas been concretized in four chapters (articles).The first part addresses issues related to econometric modeling and forecasting procedures on bothsystemic risk and high-frequency risk measures. More precisely, Chapter 2 proposes a new systemic riskmeasure used to identify systemically important financial institutions (SIFIs). Based on a componentapproach, this original measure allows to decompose the risk of the aggregate financial system whileaccounting for the firm characteristics. Chapter 3 studies the importance and certifies the validity ofintraday High Frequency Risk (HFR) measures for market risk in the special context of irregularly spacedhigh-frequency data.The second part of this thesis tackles the need to improve the estimation/prediction of volatility bydirectly including high-frequency data or realized measures of volatility. Therefore, in Chapter 4 weexamine whether high-frequency data improve the volatility forecasts accuracy, and if so, whether thereexists an optimal sampling frequency in terms of prediction. Chapter 5 studies the financial volatilityduring the global financial crisis. To this aim, we use the largest volatility shocks, as provided by therobust version of the Realized GARCH model, to identify and analyze the events having induced theseshocks during the crisis.