La tesi comprende tre saggi sul ruolo della volatilità implicita per le banche. La tesi è organizzata in tre capitoli. Capitolo I - studia il ruolo di skew e spread della volatilità implicita nel determinare i rendimenti delle azioni bancarie. Capitolo II - analizza gli effetti degli skew della volatilità implicita e della realized volatility sulla leva finanziaria delle banche. Capitolo III - si focalizza sul rapporto tra il coefficiente di liquidità delle banche e le misure per il rischio estratte dalla volatilità (skew, spread, realized volatility). / The thesis comprehends three essays on option implied volatility risk measures for banks. The thesis is organized in three chapters. Chapter I - studies the informational content for banks' stock returns in option's implied volatilities skews and spread. Chapter II - analyzes the effect of volatility risk measures (volatility skew and realized volatility) on banks' leverage. Chapter III - studies the relationship between banks' liquidity ratio and volatility risk measures.

The Autonomic Power System (APS) grand challenge was a multi-disciplinary EPSRC-funded research project that examined novel techniques that would enable the transition between today's and 2050's highly uncertain and complex energy network. Being part of the APS, this thesis reports on the sub-project 'RR2: Avoiding High-Impact Low Probability events'. The goal of RR2 is to develop new algorithms for controlling risk exposure to high-impact low probability (Hi-Lo) events through the provision of appropriate risk-sensitive control strategies. Additionally, RR2 is concerned with new techniques for identifying and modelling risk in future energy networks, in particular, the risk of Hi-Lo events. In this context, this thesis investigates two distinct problems arising from energy risk management. On the one hand, we examine the problem of finding managerial strategies for exercising the operational flexibility of energy assets. We look at this problem from a risk perspective taking into account non-linear risk preferences of energy asset managers. Our main contribution is the development of a risk-sensitive approach to the class of optimal switching problems. By recasting the problem as an iterative optimal stopping problem, we are able to characterise the optimal risk-sensitive switching strategies. As byproduct, we obtain a multiplicative dynamic programming equation for the value function, upon which we propose a numerical algorithm based on least squares Monte Carlo regression. On the other hand, we develop tools to identify and model the risk factors faced by energy asset managers. For this, we consider a class of models consisting of superposition of Gaussian and non-Gaussian Ornstein-Uhlenbeck processes. Our main contribution is the development of a Bayesian methodology based on Markov chain Monte Carlo (MCMC) algorithms to make inference into this class of models. On extensive simulations, we demonstrate the robustness and efficiency of the algorithms to different data features. Furthermore, we construct a diagnostic tool based on Bayesian p-values to check goodness-of-fit of the models on a Bayesian framework. We apply this tool to MCMC results from fitting historical electricity and gas spot price data- sets corresponding to the UK and German energy markets. Our analysis demonstrates that the MCMC-estimated models are able to capture not only long- and short-lived positive price spikes, but also short-lived negative price spikes which are typical of UK gas prices and German electricity prices. Combining together the solutions to the two problems above, we strive to capture the interplay between risk, uncertainty, flexibility and performance in various applications to energy systems. In these applications, which include power stations, energy storage and district energy systems, we consistently show that our risk management methodology offers a tradeoff between maximising average performance and minimising risk, while accounting for the jump dynamics of energy prices. Moreover, the tradeoff is achieved in such way that the benefits in terms of risk reduction outweigh the loss in average performance.

[pt] Finanças Corporativas tem como objetivo encontrar a política de investimentos e financiamentos que maximize o valor para o acionista. Baseada no modelo estático de Modigliani e Miller, a literatura recente apresenta modelos dinâmicos que buscam maior aderência à realidade. No entanto, para obter uma metodologia de solução computacionalmente tratável, duas simplificações são usualmente adotadas: (i) agentes financeiros são neutros a risco; (ii) custo de financiamento são fixos e independentes da alavancagem da empresa. Neste trabalho, é proposto um modelo de programação dinâmica estocástica para a determinação da política ótima de investimentos e financiamentos considerando acionistas avessos a risco e empresas que enfrentam incerteza na receita e custos marginais de financiamentos não-decrescentes com o nível de alavancagem da empresa. O modelo proposto é resolvido de maneira eficiente utilizando o algoritmo de Programação Dinâmica Dual Estocástica. Ao final do trabalho, são realizados estudos empíricos e análises de sensibilidade para melhor compreensão das políticas de investimentos e financiamentos das corporações. / [en] Corporate Finance is the study of investment and financing policies in order to maximize shareholder value. Based on the static model of Modigliani and Miller, recent literature presents dynamic models that seek greater adherence to reality. However, to obtain a computationally treatable solution methodology, two simplifications are usually adopted: (i) financial agents are risk neutral; (ii) cost of financing is static and independent of the company s leverage. In this work, a dynamic stochastic programming model is proposed to determine the optimum investment and financing policy, considering risk-averse shareholders and companies that face uncertainty on income and non-decreasing marginal costs of financing. The proposed model is efficiently solved using the Stochastic Dual Dynamic Programming algorithm. At the end of the study, empirical studies and sensitivity analyzes are carried out to the better understanding of corporate investment and financing policies.

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The aim of the diploma thesis is to describe risk management in a construction company. The first part of the diploma thesis is focused on theory, which deals with the explanation of basic concepts with risks and risk management in a construction company. The second, practical part addresses the risks of a specific project.

[pt] Em muitos países, uma área de Exploração e Produção de petróleo é adquirida através de um leilão. Embora o processo de liquidação do leilão seja tipicamente simples, sob a ótica do tomador de decisão a identificação da melhor oferta é complexa. Para sua valoração, deve ser pré-definido o modelo de desenvolvimento com diversas alternativas associadas, alto grau de incertezas técnicas, de mercado e operacionais, e submetido a uma determinada condição fiscal. A decisão por uma determinada alternativa gera impactos e investimentos elevados para a empresa. O trabalho proposto visa a construção de um framework para dar suporte ao processo de escolha da melhor oferta que maximize uma medida de valor para a empresa, auxiliando o tomador de decisão e considerando as incertezas envolvidas no processo. Foram utilizados os indicadores de performance apresentados na literatura: Valor Presente Líquido (VPL), Conditional Value-at-Risk, Omega e Exposição Financeira. Afim de melhor quantificar risco/benefício financeiro no processo de tomada de decisão foram construídas medidas de risco: Mean-Weighted CVaR, Mean-Weighted Double-Sided CVaR, Beta e Negative-Positive cashflow ratio. Para ilustrar a aplicabilidade do framework proposto, um experimento numérico baseado em um caso hipotético é apresentado. Em decorrência deste experimento, foi identificado que alterações na configuração da produção alteram significativamente os resultados dos indicadores. Além disso, a partir de uma ponderação entre probabilidade de ganho e o resultado do indicador Mean-Weighted CVaR, foi identificada a melhor oferta para a área, dada a condição fiscal do leilão. / [en] In many countries, an oil and gas area of Exploration and Production is acquired through an auction. Although the auction settlement process is typically simple, from the decision maker s point of view, identifying the best offer is complex. For its valuation, the development model must be pre-defined with several associated alternatives, a high degree of technical, market and operational uncertainties, and submitted to a fiscal term. The decision for a particular alternative generates high impacts and investments for the company. The proposed work aims to build a framework to support the process of choosing the best offer that maximizes a measure of value for the company, helping the decision maker and considering the uncertainties involved in the process. The performance indicators presented in the literature were used: Net Present Value (NPV), Conditional Value-at-Risk, Omega and Financial Exposure. In order to better quantify financial risk/benefit in the decisionmaking process, risk measures were constructed: Mean-Weighted CVaR, Mean- Weighted Double-Sided CVaR, Beta and Negative-Positive cashflow ratio. To illustrate the applicability of the proposed framework, a numerical experiment based on a hypothetical case is presented. As a result of this experiment, it was identified that changes in the configuration of production significantly alter the results of the indicators. In addition, from a weighting between the probability of gain and the result of the Mean-Weighted CVaR measure, the best offer for the area was identified, given the fiscal term of the bid.

Das moderne Finanzsystem ist komplex, dynamisch, hochdimensional und oftmals nicht stationär. All diese Faktoren stellen große Herausforderungen beim Messen des zugrundeliegenden Finanzrisikos dar, das speziell für Marktteilnehmer von oberster Priorität ist. Hochdimensionalität, die aus der ansteigenden Vielfalt an Finanzprodukten entsteht, ist ein wichtiges Thema für Ökonometriker. Ein Standardansatz, um mit hoher Dimensionalität umzugehen, ist es, Schlüsselvariablen auszuwählen und kleine Koeffizientenen auf null zu setzen, wie etwa Lasso. In der Finanzmarktanalyse kann eine solche geringe Annahme helfen, die führenden Risikofaktoren aus dem extrem großen Portfolio, das letztendlich das robuste Maß für finanzielles Risiko darstellt, hervorzuheben. In dieser Arbeit nutzen wir penalisierte Verfahren, um die ökonometrischen Maße für das finanzielle Risiko in hoher Dimension zu schätzen, sowohl mit nieder-, als auch hochfrequenten Daten. Mit Fokus auf dem Finanzmarkt, können wir das Risikonetzwerk des ganzen Systems konstruieren, das die Identifizierung individualspezifischen Risikos erlaubt. / Modern financial system is complex, dynamic, high-dimensional and often possibly non-stationary. All these factors pose great challenges in measuring the underlying financial risk, which is of top priority especially for market participants. High-dimensionality, which arises from the increasing variety of the financial products, is an important issue among econometricians. A standard approach dealing with high dimensionality is to select key variables and set small coefficient to zero, such as lasso. In financial market analysis, such sparsity assumption can help highlight the leading risk factors from the extremely large portfolio, which constitutes the robust measure for financial risk in the end. In this paper we use penalized techniques to estimate the econometric measures of financial risk in high dimensional, with both low-frequency and high-frequency data. With focus on financial market, we could construct the risk network of the whole system which allows for identification of individual-specific risk.

The aim of this thesis is to present new results concerning duality in scalar optimization. We show how the theory can be applied to optimization problems arising in the theory of risk measures, portfolio optimization and machine learning. First we give some notations and preliminaries we need within the thesis. After that we recall how the well-known Lagrange dual problem can be derived by using the general perturbation theory and give some generalized interior point regularity conditions used in the literature. Using these facts we consider some special scalar optimization problems having a composed objective function and geometric (and cone) constraints. We derive their duals, give strong duality results and optimality condition using some regularity conditions. Thus we complete and/or extend some results in the literature especially by using the mentioned regularity conditions, which are weaker than the classical ones. We further consider a scalar optimization problem having single chance constraints and a convex objective function. We also derive its dual, give a strong duality result and further consider a special case of this problem. Thus we show how the conjugate duality theory can be used for stochastic programming problems and extend some results given in the literature. In the third chapter of this thesis we consider convex risk and deviation measures. We present some more general measures than the ones given in the literature and derive formulas for their conjugate functions. Using these we calculate some dual representation formulas for the risk and deviation measures and correct some formulas in the literature. Finally we proof some subdifferential formulas for measures and risk functions by using the facts above. The generalized deviation measures we introduced in the previous chapter can be used to formulate some portfolio optimization problems we consider in the fourth chapter. Their duals, strong duality results and optimality conditions are derived by using the general theory and the conjugate functions, respectively, given in the second and third chapter. Analogous calculations are done for a portfolio optimization problem having single chance constraints using the general theory given in the second chapter. Thus we give an application of the duality theory in the well-developed field of portfolio optimization. We close this thesis by considering a general Support Vector Machines problem and derive its dual using the conjugate duality theory. We give a strong duality result and necessary as well as sufficient optimality conditions. By considering different cost functions we get problems for Support Vector Regression and Support Vector Classification. We extend the results given in the literature by dropping the assumption of invertibility of the kernel matrix. We use a cost function that generalizes the well-known Vapnik's ε-insensitive loss and consider the optimization problems that arise by using this. We show how the general theory can be applied for a real data set, especially we predict the concrete compressive strength by using a special Support Vector Regression problem.

The aim of this thesis is to present new results concerning duality in scalar optimization. We show how the theory can be applied to optimization problems arising in the theory of risk measures, portfolio optimization and machine learning. First we give some notations and preliminaries we need within the thesis. After that we recall how the well-known Lagrange dual problem can be derived by using the general perturbation theory and give some generalized interior point regularity conditions used in the literature. Using these facts we consider some special scalar optimization problems having a composed objective function and geometric (and cone) constraints. We derive their duals, give strong duality results and optimality condition using some regularity conditions. Thus we complete and/or extend some results in the literature especially by using the mentioned regularity conditions, which are weaker than the classical ones. We further consider a scalar optimization problem having single chance constraints and a convex objective function. We also derive its dual, give a strong duality result and further consider a special case of this problem. Thus we show how the conjugate duality theory can be used for stochastic programming problems and extend some results given in the literature. In the third chapter of this thesis we consider convex risk and deviation measures. We present some more general measures than the ones given in the literature and derive formulas for their conjugate functions. Using these we calculate some dual representation formulas for the risk and deviation measures and correct some formulas in the literature. Finally we proof some subdifferential formulas for measures and risk functions by using the facts above. The generalized deviation measures we introduced in the previous chapter can be used to formulate some portfolio optimization problems we consider in the fourth chapter. Their duals, strong duality results and optimality conditions are derived by using the general theory and the conjugate functions, respectively, given in the second and third chapter. Analogous calculations are done for a portfolio optimization problem having single chance constraints using the general theory given in the second chapter. Thus we give an application of the duality theory in the well-developed field of portfolio optimization. We close this thesis by considering a general Support Vector Machines problem and derive its dual using the conjugate duality theory. We give a strong duality result and necessary as well as sufficient optimality conditions. By considering different cost functions we get problems for Support Vector Regression and Support Vector Classification. We extend the results given in the literature by dropping the assumption of invertibility of the kernel matrix. We use a cost function that generalizes the well-known Vapnik's ε-insensitive loss and consider the optimization problems that arise by using this. We show how the general theory can be applied for a real data set, especially we predict the concrete compressive strength by using a special Support Vector Regression problem.

Nesta dissertação, o modelo de seleção de carteiras de Markowitz será estendido com uma análise em tempo discreto e hipóteses mais realísticas. Um produto tensorial finito de densidades Erlang será usado para aproximar a densidade de probabilidade multivariada dos retornos discretos uniperiódicos de ativos dependentes. A Erlang é um caso particular da distribuição Gama. Uma mistura finita pode gerar densidades multimodais não-simétricas e o produto tensorial generaliza este conceito para dimensões maiores. Assumindo que a densidade multivariada foi independente e identicamente distribuída (i.i.d.) no passado, a aproximação pode ser calibrada com dados históricos usando o critério da máxima verossimilhança. Este é um problema de otimização em larga escala, mas com uma estrutura especial. Assumindo que esta densidade multivariada será i.i.d. no futuro, então a densidade dos retornos discretos de uma carteira de ativos com pesos não-negativos será uma mistura finita de densidades Erlang. O risco será calculado com a medida Downside Risk, que é convexa para determinados parâmetros, não é baseada em quantis, não causa a subestimação do risco e torna os problemas de otimização uni e multiperiódico convexos. O retorno discreto é uma variável aleatória multiplicativa ao longo do tempo. A distribuição multiperiódica dos retornos discretos de uma seqüência de T carteiras será uma mistura finita de distribuições Meijer G. Após uma mudança na medida de probabilidade para a composta média, é possível calcular o risco e o retorno, que levará à fronteira eficiente multiperiódica, na qual cada ponto representa uma ou mais seqüências ordenadas de T carteiras. As carteiras de cada seqüência devem ser calculadas do futuro para o presente, mantendo o retorno esperado no nível desejado, o qual pode ser função do tempo. Uma estratégia de alocação dinâmica de ativos é refazer os cálculos a cada período, usando as novas informações disponíveis. Se o horizonte de tempo tender a infinito, então a fronteira eficiente, na medida de probabilidade composta média, tenderá a um único ponto, dado pela carteira de Kelly, qualquer que seja a medida de risco. Para selecionar um dentre vários modelos de otimização de carteira, é necessário comparar seus desempenhos relativos. A fronteira eficiente de cada modelo deve ser traçada em seu respectivo gráfico. Como os pesos dos ativos das carteiras sobre estas curvas são conhecidos, é possível traçar todas as curvas em um mesmo gráfico. Para um dado retorno esperado, as carteiras eficientes dos modelos podem ser calculadas, e os retornos realizados e suas diferenças ao longo de um backtest podem ser comparados. / In this thesis, Markowitz’s portfolio selection model will be extended by means of a discrete time analysis and more realistic hypotheses. A finite tensor product of Erlang densities will be used to approximate the multivariate probability density function of the single-period discrete returns of dependent assets. The Erlang is a particular case of the Gamma distribution. A finite mixture can generate multimodal asymmetric densities and the tensor product generalizes this concept to higher dimensions. Assuming that the multivariate density was independent and identically distributed (i.i.d.) in the past, the approximation can be calibrated with historical data using the maximum likelihood criterion. This is a large-scale optimization problem, but with a special structure. Assuming that this multivariate density will be i.i.d. in the future, then the density of the discrete returns of a portfolio of assets with nonnegative weights will be a finite mixture of Erlang densities. The risk will be calculated with the Downside Risk measure, which is convex for certain parameters, is not based on quantiles, does not cause risk underestimation and makes the single and multiperiod optimization problems convex. The discrete return is a multiplicative random variable along the time. The multiperiod distribution of the discrete returns of a sequence of T portfolios will be a finite mixture of Meijer G distributions. After a change of the distribution to the average compound, it is possible to calculate the risk and the return, which will lead to the multiperiod efficient frontier, where each point represents one or more ordered sequences of T portfolios. The portfolios of each sequence must be calculated from the future to the present, keeping the expected return at the desired level, which can be a function of time. A dynamic asset allocation strategy is to redo the calculations at each period, using new available information. If the time horizon tends to infinite, then the efficient frontier, in the average compound probability measure, will tend to only one point, given by the Kelly’s portfolio, whatever the risk measure is. To select one among several portfolio optimization models, it is necessary to compare their relative performances. The efficient frontier of each model must be plotted in its respective graph. As the weights of the assets of the portfolios on these curves are known, it is possible to plot all curves in the same graph. For a given expected return, the efficient portfolios of the models can be calculated, and the realized returns and their differences along a backtest can be compared.