[pt] Muitos dos modelos de simulação de cenários de vazões, necessários para o planejamento e operação de setores elétricos, são construídos sob hipóteses rígidas. Isto pode restringir sua capacidade de representar dependências não-lineares e\ou distribuições não usuais. Cópulas superam estas limitações. Elas possibilitam que o comportamento marginal das variáveis seja modelado separadamente da estrutura de dependência do vetor aleatório. Além do mais, podem representar os mais diversos tipos de associações. Isto posto, esta tese apresenta 3 artigos onde modelos de cópulas são desenvolvidos visando a simulação de cenários de vazões. No primeiro artigo, propomos um modelo periódico de cópulas vine espaciais para simulação multivariada. As principais contribuições são a extensão para o caso periódico dos modelos de cópulas vine espaciais; a drástica redução do número de parâmetros; o desenvolvimento de um modelo não linear multivariado para simulação de cenários de vazões que incorpora a dependência temporal, a dependência espacial, a variação sazonal e o elevado número de usinas (alta dimensão). No segundo artigo, realizamos algumas modificações no modelo periódico espacial proposto que resultam em uma menor complexidade sem perda de performance. No terceiro artigo, propomos uma metodologia baseada em cópulas vine para modelar a dependência temporal de séries periódicas uni variadas de vazões. Dentre as contribuições destaca-se a construção de uma versão não-linear dos modelos periódicos autorregressivos (PAR(p)) onde a dependência temporal de qualquer ordem pode ser considerada; a possibilidade da incorporação de efeitos lineares e não-lineares; um modelo que não simula cenários com valores negativos; a flexibilidade para se modelar as distribuições marginais mensais. / [en] Many streamflow scenario simulation models, which are needed for the planning and operation of energy systems, are built on rigid assumptions. This may limit their ability to represent nonlinear dependencies and/or nonstandard distribution functions. Copulas overcome these drawbacks and represent a flexible tool for modeling multivariate distributions. They enable the modeling of the marginal behavior of variables separately from the dependence structure of a random vector. Moreover, they can represent any type of association. This thesis is composed of three working papers, wherein copula-based models are proposed, objectifying the simulation of streamflow scenarios. In the first working paper, a periodic spatial copula model is proposed to simulate multivariate streamflow scenarios. The main contributions include periodic extension of the spatial vine copulas; a distinct reduction in the number of parameters; and the development of a multivariate nonlinear model for streamflow scenario generation that incorporates time dependence, spatial dependence, and seasonal variation, and accounts for the dimensionality of the problem (high number of hydroelectric power plants). In the second working paper, some modifications are made to the periodic spatial model, resulting in lower complexity without the loss of performance. In the third working paper, a methodology based on the vine copula is proposed to model the temporal dependence structures in a univariate periodic streamflow time series. Among the contributions, the construction of a nonlinear version of the periodic autoregressive model (PAR(p)) is highlighted. The possibility of modeling linear and nonlinear effects and the flexibility of modeling the monthly marginal distributions are highlighted as well. This model does not simulate negative values.

For an equity-linked insurance, the death benefit is linked to the performance of the company’s investment portfolio. Hence, both mortality risk and equity return shall be considered for pricing such insurance. Several studies have found some dependence between mortality improvement and economy growth. In this thesis, we showed that American mortality rate and Dow Jones Industrial Average (DJIA) index price are negatively dependent by using several copulas to define the joint distribution. Then, we used these copulas to forecast mortality rates and index prices, and calculated the payoffs of a 10-year term equity-linked insurance. We showed that the predicted insurance payoffs will be smaller if dependence between mortality and index price is taken into account. / October 2016

The aim of this thesis is the thorough description of the copula theory. It deals with the theory's basic definitions, classes and characteristics. In addition, relations between copulas and dependence measures are explained. Furthermore, we evaluate the possibilities of copula's parametres estimation and selecting the right copula for real data. Then, the copula theory is interconnected with the basic risk measures in finance. We describe the elementary categorization of financial risks and standard risk measurement approaches. We also define basic risk measures with the emphasis on value at risk. Lastly, we present a real data case study of a selected portfolio.

D.Comm. / Copulas provide a useful way to model different types of dependence structures explicitly. Instead of having one correlation number that encapsulates everything known about the dependence between two variables, copulas capture information on the level of dependence as well as whether the two variables exhibit other types of dependence, for example tail dependence. Tail dependence refers to the instance where the variables show higher dependence between their extreme values. A copula is defined as a multivariate distribution function with uniform marginals. A useful class of copulas is known as Archimedean copulas that are constructed from generator functions with very specific properties. The main aim of this thesis is to construct multivariate Archimedean copulas by nesting different bivariate Archimedean copulas using the vine construction approach. A characteristic of the vine construction is that not all combinations of generator functions lead to valid multivariate copulas. Established research is limited in that it presents constraints that lead to valid multivariate copulas that can be used to model positive dependence only. The research in this thesis extends the theory by deriving the necessary constraints to model negative dependence as well. Specifically, it ensures that the multivariate copulas that are constructed from bivariate copulas that capture negative dependence, will be able to capture negative dependence as well. Constraints are successfully derived for trivariate copulas. It is, however, shown that the constraints cannot easily be extended to higher-order copulas. The rules on the types of dependence structures that can be nested are also established. A number of practical applications in the financial markets where copula theory can be utilized to enhance the more established methodologies, are considered. The first application considers trading strategies based on statistical arbitrage where the information in the bivariate copula structure is utilised to identify trading opportunities in the equity market. It is shown that trading costs adversely affect the profits generated. The second application considers the impact of wrong-way risk on counterparty credit exposure. A trivariate copula is used to model the wrong-way risk. The aim of the analysis is to show how the theory developed in this thesis should be applied where negative correlation is present in a trivariate copula structure. Approaches are considered where conditional and unconditional risk driver scenarios are derived by means of the trivariate copula structure. It is argued that by not allowing for wrong-way risk, a financial institution’s credit pricing and regulatory capital calculations may be adversely affected. The final application compares the philosophy behind cointegration and copula asset allocation techniques to test which approach produces the most profitable index-tracking portfolios over time. The copula asset allocation approach performs well over time; however, it is very computationally intensive.

Começamos por estudar fronteiras para uma classe especial de medidas de risco quantis, chamadas medidas de risco distorcidas. A hipótese básica é que o conhecimento da estrutura de dependência (ou seja, da distribuição conjunta) da carteira de riscos é incompleta, fazendo com que não seja possível obter um valor exato para tais medidas. Isso é muito comum na prática. Fornecemos duas formas de obter tais limites nessa situação, apresentando seus prós e contras. A modelagem de risco, em um cenário de desconhecimento total ou parcial da distribuição conjunta dos mesmos, geralmente faz uso de cópulas. Entretanto, as cópulas vêm sendo alvo de críticas na literatura recente. Um dos motivos é que as mesmas desprezam o comportamento marginal e comprimem os dados no quadrado unitário. Dentro desse cenário, apresentamos uma função que pode ser vista como uma alternativa e complemento ao uso de cópulas: função de dependência de Sibuya. / We begin our work studying an special class of quantile risk measures, known as distorted risk measures. The basic assumption is that the risk manager does not know the complete dependence structure (that is, the risks\'s joint distribution) embedded in the risk\'s portfolio, what makes the exact computation of the risk measure an impossible task. This is a common scenario in practical problems. We present two approaches to compute bounds for the distorted risk measures in such situation, underlining the pros and cons of each one. In risk modeling, in the absence of complete knowledge regarding their joint distribution, one often relies on the copula function approach. However, copulas have been criticized in recent publications mostly because it ignores the marginal behavior and smash the data into the unity square. In order to overcome such problems we present and alternative and complement to the copula approach: the Sibuya dependence function.

Começamos por estudar fronteiras para uma classe especial de medidas de risco quantis, chamadas medidas de risco distorcidas. A hipótese básica é que o conhecimento da estrutura de dependência (ou seja, da distribuição conjunta) da carteira de riscos é incompleta, fazendo com que não seja possível obter um valor exato para tais medidas. Isso é muito comum na prática. Fornecemos duas formas de obter tais limites nessa situação, apresentando seus prós e contras. A modelagem de risco, em um cenário de desconhecimento total ou parcial da distribuição conjunta dos mesmos, geralmente faz uso de cópulas. Entretanto, as cópulas vêm sendo alvo de críticas na literatura recente. Um dos motivos é que as mesmas desprezam o comportamento marginal e comprimem os dados no quadrado unitário. Dentro desse cenário, apresentamos uma função que pode ser vista como uma alternativa e complemento ao uso de cópulas: função de dependência de Sibuya. / We begin our work studying an special class of quantile risk measures, known as distorted risk measures. The basic assumption is that the risk manager does not know the complete dependence structure (that is, the risks\'s joint distribution) embedded in the risk\'s portfolio, what makes the exact computation of the risk measure an impossible task. This is a common scenario in practical problems. We present two approaches to compute bounds for the distorted risk measures in such situation, underlining the pros and cons of each one. In risk modeling, in the absence of complete knowledge regarding their joint distribution, one often relies on the copula function approach. However, copulas have been criticized in recent publications mostly because it ignores the marginal behavior and smash the data into the unity square. In order to overcome such problems we present and alternative and complement to the copula approach: the Sibuya dependence function.

Thesis (Ph. D.)--University of California, San Diego, 2002. / Vita. Includes bibliographical references.

In financial risk management it is essential to be able to model dependence in markets and portfolios in an accurate and efficient way. A high positive dependence between assets in a portfolio can be devastating, especially in times of crises, since losses will most likely occur at the same time in all assets for such a portfolio. The dependence is therefore directly linked to the risk of the portfolio. The risk can be estimated by several different risk measures, for example Value-at-Risk and Expected shortfall. This paper studies some different ways to measure risk and model dependence, both in a theoretical and empirical way. The main focus is on copulas, which is a way to model and construct complex dependencies. Copulas are a useful tool since it allows the user to separately specify the marginal distributions and then link them together with the copula. However, copulas can be quite complex to understand and it is not trivial to know which copula to use. An implemented copula model might give the user a "black-box" feeling and a severe model risk if the user trusts the model too much and is unaware of what is going. Another model would be to use the linear correlation which is also a way to measure dependence. This is an easier model and as such it is believed to be easier for all users to understand. However, linear correlation is only easy to understand in the case of elliptical distributions, and when we move away from this assumption (which is usually the case in financial data), some clear drawbacks and pitfalls become present. A third model, called historical simulation, uses the historical returns of the portfolio and estimate the risk on this data without making any parametric assumptions about the dependence. The dependence is assumed to be incorporated in the historical evolvement of the portfolio. This model is very easy and very popular, but it is more limited than the previous two models to the assumption that history will repeat itself and needs much more historical observations to yield good results. Here we face the risk that the market dynamics has changed when looking too far back in history. In this paper some different copula models are implemented and compared to the historical simulation approach by estimating risk with Value-at-Risk and Expected shortfall. The parameters of the copulas are also investigated under calm and stressed market periods. This information about the parameters is useful when performing stress tests. The empirical study indicates that it is difficult to distinguish the parameters between the stressed and calm market period. The overall conclusion is; which model to use depends on our beliefs about the future distribution. If we believe that the distribution is elliptical then a correlation model is good, if it is believed to have a complex dependence then the user should turn to a copula model, and if we can assume that history will repeat itself then historical simulation is advantageous.

Numerous authors note failure of private insurance markets to provide affordable and comprehensive crop insurance. Economic logic suggests that index contracts potentially may have some advantages when compared with traditional (farm based) crop insurance. It is also a matter of common knowledge that weather is an important production factor and at the same time one of the greatest sources of risk in agriculture. Hence introduction of crop insurance contracts, based on weather indexes, might be a reasonable approach to mitigate problems, associated with traditional crop insurance products, and possibly lower the cost of insurance for end users. In spite of the fact that before the financial crisis of 2008-09 market for weather derivatives was the fastest growing derivatives market in the USA, agricultural producers didn’t express much interest in application of weather derivatives to management of their systematic risk. There are several reasons for that, but the most important one is the presence of high basis risk, which is represented by its two major components: technological (i.e. goodness of fit between yield and weather index) and geographical basis. Majority of the researchers is focusing either on pricing of weather derivatives or on mitigation of geographical basis risk. At the same time the number of papers researching possible ways to decrease technological basis is quite limited, and always assumes linear dependency between yields and weather variables, while estimating the risk reducing efficiency of weather contracts, which is obviously large deviation from reality. The objective of this study is to estimate the risk reducing efficiency of crop insurance contracts, based on weather derivatives (indexes) in the state of Texas. The distributions of representative farmer’s profits with the proposed contracts are compared to the distributions of profits without a contract. This is done to demonstrate the risk mitigating effect of the proposed contracts. Moreover the study will try to account for a more complex dependency structures between yields and weather variables through usage of copulas, while constructing joint distribution of yields and weather data. Selection of the optimal copula will be implemented in the out-of-sample efficient framework. An effort will be done to identify the most relevant periods of year, when weather has the most significant influence on crop yields, which should be included in the model, and to discover the most effective copula to model joint weather/yield risk. Results suggest that effective insurance of crop yields in the state of Texas by the means of proposed weather derivatives is possible. Besides, usage of data-mining techniques allows for more accurate selection of the time periods to be included in the model than ad hoc procedure previously used in the literature. Finally selection of optimal copula for modeling of joint weather/yield distribution should be crop and county specific, while in general Clayton and Frank copula of Archimedean copula family provide the best out-of-sample metric results.

Thesis (Ph. D.)--University of California, San Diego, 2007. / Title from first page of PDF file (viewed August 7, 2007). Available via ProQuest Digital Dissertations. Vita. Includes bibliographical references.