We model Normal Inverse Gaussian distributed log-returns with the assumption of stochastic volatility. We consider different methods of parametrization of returns and following the paper of Lindberg, [21] we assume that the volatility is a linear function of the number of trades. In addition to the Lindberg’s paper, we suggest daily stock volumes and amounts as alternative measures of the volatility. As an application of the models, we perform Value-at-Risk and Expected Tail Loss predictions by the Lindberg’s volatility model and by our own suggested model. These applications are new and not described in the literature. For better understanding of our caluclations, programmes and simulations, basic informations and properties about the Normal Inverse Gaussian and Inverse Gaussian distributions are provided. Practical applications of the models are implemented on the Nasdaq-OMX, where we have calculated Value-at-Risk and Expected Tail Loss for the Ericsson B stock data during the period 1999 to 2004.

Routing and designing are essential for transportation networks. With effective routing and designing policies, transportation networks can work safely and efficiently. There are two transportation problems: hazardous materials (hazmat) transportation and warehouse logistics. This dissertation addresses the routing of networks for both problems. For hazmat transportation, the routing can be regulated via network design. Due to catastrophic consequences of potential accidents in hazmat transportation, a risk-averse approach for routing is necessary. In this dissertation, we consider spectral risk measures, for risk-averse hazmat routing. In addition, we introduce a network design problem to select a set of closed road segments for hazmat traffic with conditional value-at-risk (CVaR) to regulate hazmat routing. In warehouses, the routing of electric forklifts with sufficient battery levels is for material handling. The optimization model of dynamic wireless charging lane location is proposed under the workflow congestion in parallel-aisle warehouses. Considering the uncertainty of demands, the wireless charging lane location problem is formulated as a two-stage stochastic programming model. We confirm the efficiency of the proposed algorithms in solving these problems and the key advantages of use the proposed routing and designing policies via case studies.

When measuring market risk, credit institutions and Alternative Investment Fund Managers may deviate from equally weighting historical data in their Value-at-Risk calculation and instead use an exponential time series weighting. The use of expo-nential weighting in the Value-at-Risk calculation is very popular because it takes into account changes in market volatility (immediately) and can therefore quickly adapt to VaR. In less volatile market phases, this leads to a reduction in VaR and thus to lower own funds requirements for credit institutions. However, in the ex-ponential weighting a high volatility in the past is quickly forgotten and the VaR can be underestimated when using exponential weighting and the VaR may be un-derestimated. To prevent this, credit institutions or Alternative Investment Fund Managers are not completely free to choose a weighting (decay) factor. This article describes the legal requirements and deals with the calculation of the permissible weighting factor. As an example we use the exchange rate between Euro and Polish zloty to estimate the Value-at-Risk. We show the calculation of the weighting factor with two different approaches. This article also discusses exceptions to the general legal requirements.

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.

The study has examined the performance of six different specifications of Recurrent Neural Networks designed to predict Value at Risk at the one and five percent level. The models have been tested on the OMX30 stock index, the SEK/EUR exchange rate and the Class A Berkshire-Hathaway stock using a GARCH expanding window as baseline model. The proposed Neural Networks show decent predictive performance, serving as an indication of the potential use of Recurrent Neural Networks’ predictive capabilities of VaR. In three cases out of six does a proposed network outperform the baseline GARCH. However, when comparing the proposed models’ performance with the baseline GARCH, it is evident that GARCH on average is more precise and consistent in its predictions. Furthermore, the results show that the Neural Networks’ performance is very sensitive to the hyperparameter tuning, and that finding a model specification that performs well on both in-sample and out-of-sample data is rather difficult, as well as finding a single specification that performs acceptably on several data sets. Given the narrow selection of hyperparameters tuned, the fact that one of the proposed neural network models managed to beat the high performing GARCH in three out of six cases suggests that the subject could benefit from further studies. Future studies are recommended to extend the scope of hyperparameter tuning.

Portfolio Management is the process of allocating an investor's wealth to in­ vestment opportunities over a given planning period. Not only should Portfolio Management be treated within a multi-period framework, but one should also take into consideration the stochastic nature of related parameters. After a short review of key concepts from Finance Theory, e.g. utility function, risk attitude, Value-at-rusk estimation methods, a.nd mean-variance efficiency, this work describes a framework for the formulation of the Portfolio Management problem in a Stochastic Programming setting. Classical solution techniques for the resolution of the resulting Stochastic Programs (e.g. L-shaped Decompo­ sition, Approximation of the probability function) are presented. These are discussed within both the two-stage and the multi-stage case with a special em­ phasis on the former. A description of how Importance Sampling and EVPI are used to improve the efficiency of classical methods is presented. Postoptimality Analysis, a sensitivity analysis method, is also described. / Statistics / M. Sc. (Operations Research)

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.

本文以台灣股價加權指數，使用 AR(3)-GJR-GRACH(1,1) 模型，白噪音假設為 Normal 、 Skew-Normal 、 Student t 、 skew-t 、 EPD 、 SEPD 、與 AEPD 等七種分配。著重於兩個部份，(一) Student t 分配一族與 EPD 分配一族在模型配適與風險值估計的比較；(二) 預測風險值區分為低震盪與高震盪兩個區間，比較不同分配在兩區間預測風險值的差異。 實證分析顯示， t 分配一族與 EPD 分配一族配適的結果，無論是只考慮峰態 ( t 分配與 EPD 分配) ，或者加入影響偏態的參數 ( skew-t 分配與 SEPD 分配) ， t 分配一族的配適程度都較 EPD 分配一族為佳。更進一步考慮分配兩尾厚度不同的 AEPD 分配，配適結果為七種分配中最佳。 風險值的估計在低震盪的區間，常態分配與其他厚尾分配皆能通過回溯測試，採用厚尾分配效果不大；在高震盪的區間，左尾風險值回溯測試結果，常態分配與其他厚尾分配皆無法全數通過，但仍以 AEPD 分配為最佳。最後比較損失函數，左尾風險值估計以 AEPD 分配為最佳，右尾風險值則無一致的結果。因此我們認為 AEPD 分配可作為風險管理有用的工具。

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]

This thesis provides an analysis of systemic risk in the US banking sector. We use conditional value at risk (∆CoVaR), marginal expected shortfall (MES) and cross-quantilogram (CQ) to statistically measure tail-dependence in return series of individual institutions and the system as a whole. Wavelet multireso- lution analysis is used to study systemic risk in the time-frequency domain. De- composition of returns on different scales allows us to isolate cycles of 2-8 days, 8-32 days and 32-64 days and analyze co-movement patterns which would oth- erwise stay hidden. Empirical results demonstrate that filtering out short-term noise from the return series improves the forecast power of ∆CoVaR. Eventu- ally, we investigate the connection between statistical measures of systemic risk and fundamental characteristics of institutions (size, leverage, market to book ratio) and conclude that size is the most robust determinant of systemic risk.