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 aim of this diploma thesis is to analyze ways of Value at Risk calculation. Its core is to get a suitable model that could most appropriately reflect the probability distribution of returns of the Czech stock portfolio that we have generated. In this thesis we find out that the returns follow unbounded distribution which was first described by Johnson (1949). Since we detect that returns are correlated we have to apply appropriate autoregressive process that removes this dependency. In the empirical part we discover an inability of models based on assumptions of normality, to correctly predict the Value at Risk. Historical simulation methods, which have promising backtesting results, are rejected because of the slow adaptation to the recent changes in the market. However, we find a way how to implement Johnson SU distribution into the GARCH model. This model, which passes all the tests, is thus able to predict Value at Risks of the portfolio most accurately. JEL Classification: C16, C22, G11 Keywords: Market risk, Value at Risk, Risk management, Johnson SU distribution

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.

The main focus of this work is on hedging of currency risks with special emphasis on the case of Czech export. In the first chapter, I create a motivation for further studying of the problem. I describe the state of export industries and the economy as a whole and how these aspects are connected to the exchange rates. In the second chapter, I explain how firms create their assumptions about future exchange rates. I also run a Monte Carlo analysis on historical data and come with predictions of my own. In the third chapter, I am discussing the relevance of using VaR models for estimating the maximum possible loss of funds due to unwanted moves in the exchange rate. Furthermore, I describe various instruments usable for hedging of currency exposure including forwards, options, swaps and other derivatives. In the final chapter of this work, I am asking financial and sales directors of 51 Czech firms about how currency risks influence their businesses and how they protect themselves against these threats.

We propose a Markov chain model for credit rating changes. We do not use any distributional assumptions on the asset values of the rated companies but directly model the rating transitions process. The parameters of the model are estimated by a maximum likelihood approach using historical rating transitions and heuristic global optimization techniques. We benchmark the model against a GLMM model in the context of bond portfolio risk management. The proposed model yields stronger dependencies and higher risks than the GLMM model. As a result, the risk optimal portfolios are more conservative than the decisions resulting from the benchmark model.

Neste trabalho, apresentamos alguns métodos para avaliação das previsões do Valor em Risco (VaR). Estes métodos testam um tipo de eficiência, denominada cobertura condicional correta. O poder empírico e a probabilidade do erro de tipo I são comparados através de simulações de Monte Carlo. Além disso, avaliamos um novo método de previsão do VaR, o qual é aplicado nos retornos diários do Ibovespa. Os resultados obtidos mostram que a nova classe de testes, baseados em uma regressão Weibull discreta, em muitos casos, tem poder empírico maior comparando com outros métodos apresentados neste trabalho. / In this paper, we present some procedures for assessing forecasts for the Value at Risk (VaR). These procedures test a type of efficiency, referred as correct conditional coverage. The empirical power and type I error probability are compared through a Monte Carlo simulation. The results show that a new class of tests based on a discrete Weibull regression in most cases has greater power empirical to other methods available in this paper.

Western countries, institutions, and people from all walks of land, including Africans, have carried the notion that it is riskier to invest in African countries compared to countries in other continents. This study verified if that notion is empirically established or it is just a mere notion born out of people's imagination and unfounded belief. The study did select one special metal mining company listed on the New York stock exchange from every continent using a systematic random sampling of period five. All these stocks' data were daily data spanning the period 2003-06 - 2020:06 obtained from Yahoo Finance. The said duration was used for the analysis because one of the companies selected for the study only had stock data starting from 2003-06-25. Because of Generalized Autoregressive Conditionally Heteroscedastic (GARCH) ability to model the conditional randomly varying volatility, the study trained several of them for a different order of the GARCH terms σ2, and the order of the ARCH terms ε2 and for different distributions. Based on the AIC and BIC, the GARCH model that best fitted the data was GARCH (1,1), thus order one of the GARCH terms σ2 and order one of the ARCH terms ε2 based on student-t innovation. The study proceeded to estimate the risk measure using three of the approaches (risk metrics, Block Maxima Method under extreme value situation, and Generalized Pareto Distribution (GPD) for the tail ends of the distribution). None of the approaches or methods used in calculating VaR or conditional VaR (ES) of the stocks supported the conventional beliefs and age long-held purported gospel that African counties are the riskiest to invest on earth. In the risk metrics approach, the African stock was second riskiest to European stock. At the same time, in extreme value situations, it was third to European and South American; with GPD, it was third once again to South American and European stock. The study proceeded to verify if this founding were statistically significant. Applying analysis of variance (ANOVA), found that none of the differences established above is statistically significant. Meaning, statistically, the value and conditional value of one's investment that will be at risk is not different based on the investment's continental location. Thus, it is not statistically riskier to invest in one continent than the other.

This thesis presents two Models of portfolio optimization, namely the Markowitz Mean Variance Optimization Model and the Rockefeller and Uryasev CVaR Optimization Model. It then presents an application of these models to a portfolio of clean energy assets for optimal allocation of financial resources in terms of maximum returns and low risk. This is done by writing GAMS programs for these optimization problems. An in-depth analysis of the results is conducted, and we see that the difference between both models is not very significant even though these results are data-specific.

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.