[pt] Em Fleming, Kirby e Ostdiek (2001), encontram-se evidências de que a utilização de modelos de previsão da volatilidade, possui valor econômico significante quando se compara simplesmente com a matriz de variância incondicional, num arcabouço de otimização de portfólio. Indo além, este trabalho propõem averiguar se os modelos mais complexos de Correlação Condicional Constante (CCC) e Dinâmica (DCC) sugeridos respectivamente por Bollerslev (1990) e Engle (2002) podem oferecer melhores resultados. Os resultados encontrados são dependentes da preferência do investidor. Um investidor mais avesso ao risco, terá maior utilidade ao empregar o modelo DCC e CCC quando comparado ao simples modelo da média móvel com decaimento exponencial, popularizados por RiskMetrics. Isso ocorre porque os modelos DCC e CCC apresentam desvio padrão e retorno geralmente inferiores. Ainda, não é possível afirmar como em Fleming, Kirby e Ostdiek (2001) que a utilização de modelos de previsão da volatilidade, possui valor econômico significante. / [en] At Fleming, Kirby e Ostdiek (2001), evidences are found that volatility timming models, have signicant economic value when comparing with the simple unconditional variance matrix, in a framework of portfolio optimization. Going further, this work analyze if the more complex Constant (CCC) and Dynamic (DCC) Conditional Corrrelation models, suggested respectivily by Bollerslev (1990) and Engle (2002) can have a higher performance. The results found depend on the investor´s preference. A more risk averse investor has a higher utility level employing the DCC and CCC models when comparing with the simple exponencial moving avarage model, popularized by RiskMetrics. This happens because the DCC and CCC models usually have smaller standard deviation and return. Futhermore, it is not possible to assert, like at Fleming, Kirby e Ostdiek (2001), that volatility timming models have higher economic value.

Value at Risk (VaR) är en finansiell metod för att skatta risker och som används i stor utsträckning av banker och företag. VaR beräknar att en eventuell förlust inte skall överstiga ett visst belopp med 95/99 procents konfidens. Denna uppsats syfte är att undersöka om VaR kan appliceras på en svensk aktie när Riskmetrics-modellen (IGARCH) skattar volatiliteten på aktien trots oro på den finansiella marknaden. Undersökningen genomfördes på Volvos B-aktie med data från perioden 2003-01-01 till 201 2-12-31. Vi genererade enstegsprognoser över den potentiella förlusten (VaR) givet en fiktiv investering av 10 000 000 SEK. Det estimerade VaR jämfördes sedan med de verkliga historiska utfallen. Resultaten visade att VaR med Riskmetrics-metoden lyckas täcka den verkliga förlusten i 96.31 procent av fallen. Detta resultat tyder på att Riskmetrics lyckas att skatta volatiliteten även under oroligheter, dels på den finansiella marknaden och dels inom företaget.

Inline with the third pillar of the Basel accords, quantitative market risk measurements are investigate and evaluated comparing JP Morgan’s RiskMetrics and Bollerslev’s GARCH with the Peek over Threshold and Block Maxima approaches from the Extreme Value Theory framework. Value-at-Risk and Expected Shortfall (Conditional Value-at-Risk), with 95% and 99% confidence, is predicted for 25 years of the OMXS30. The study finds Bollerslev’s suggested t distribution to be a more appropriate distributional assumption, but no evidence to prefer the GARCH to the RiskMetrics. The more demanding Extreme Value Theory procedures trail behind as they are found wasteful of data and more difficult to backtest and therefore evaluate.

Stock market volatility has been an important subject in the finance literature for which now an enormous body of research exists. Volatility modelling and forecasting have been in the epicentre of this line of research and although more than a few models have been proposed and key parameters on improving volatility forecasts have been considered, finance research has still to reach a consensus on this topic. This thesis enters the ongoing debate by carrying out empirical investigations by comparing models from the current pool of models as well as exploring and proposing the use of further key parameters in improving the accuracy of volatility modelling and forecasting. The importance of accurately forecasting volatility is paramount for the functioning of the economy and everyone involved in finance activities. For governments, the banking system, institutional and individual investors, researchers and academics, knowledge, understanding and the ability to forecast and proxy volatility accurately is a determining factor for making sound economic decisions. Four are the main contributions of this thesis. First, the findings of a volatility forecasting model comparison reveal that the GARCH genre of models are superior compared to the more ‘simple' models and models preferred by practitioners. Second, with the use of backward recursion forecasts we identify the appropriate in-sample length for producing accurate volatility forecasts, a parameter considered for the first time in the finance literature. Third, further model comparisons are conducted within a Value-at-Risk setting between the RiskMetrics model preferred by practitioners, and the more complex GARCH type models, arriving to the conclusion that GARCH type models are dominant. Finally, two further parameters, the Volatility Index (VIX) and Trading Volume, are considered and their contribution is assessed in the modelling and forecasting process of a selection of GARCH type models. We discover that although accuracy is improved upon, GARCH type forecasts are still superior.

This diploma thesis studies extreme value theory and its application in finan- cial risk management, when focusing on computation of well-known risk measure - Value at Risk (VaR). The first part of the thesis reviews theoretical background. In particular, it rigorously discusses the extreme value theory when emphasi- zing fundamentals theorems and their consequences followed by the summary of methods based on this theory, specifically, Block Maxima method, Hill met- hod and Peaks over Threshold method. Moreover, specific issues that may arise in such applications and ways how to deal with these problems are described. The second part of the thesis contains extensive empirical study, which together with theoretical foundings applies each of the examined method to real market data of the closing prices of Dow Jones Industrial Average stock index, stocks of JPMorgan and stock index Russell 2000 in order to compare methods based on extreme value theory together with the classic methodology RiskMetrics. 1

Este trabalho consiste em um estudo comparativo de diversos modelos para cálculo do Valor em Risco de um portifólio. São comparados modelos que consideram a série univariada de log-retornos do portifólio versus mo- delos multivariados, que consideram as séries de log-retornos de cada ativo que compõe o portifólio e suas correlações condicionais. Além disso, são testados modelo propostos recentemente, que possuem pouca literatura a respeito, como o PS-GARCH e o VARMA-GARCH. Também propomos um novo modelo, que utiliza o resultado acumulado do portifólio nos últimos dias como variável exógena. Os diferentes modelos são avaliados em termos de sua adequação às exigëncias do Acordo de Basileia e seu impacto financeiro, em um período que inclui épocas de alta volatilidade. De forma geral, não foram notadas grandes diferenças de performance entre modelos univariados e multivariados. Os modelos mais complexos mostraram-se mais eficientes, produzindo resultados satisfatórios inclusive em tempos de crise. / The present work consists of a comparative study of several portfolio Value-at-Risk models. Univariate models, which consider only the portfolio log-returns series, are compared to multivariate models, which consider the log-returns series of each asset individually and their conditional correlations. Additionally, recently proposed models such as PS-GARCH and VARMA-GARCH are tested. We also propose a new model that uses past cumulative returns as exogenous variables. All models are evaluated in terms of their compliance to Basel Accord and financial impact, in period that includes high volatility times. In general, univariate and multivariate models performed similarly. More complex models yielded more accurate results, with satisfactory performance including in crisis periods.

Este trabalho consiste em um estudo comparativo de diversos modelos para cálculo do Valor em Risco de um portifólio. São comparados modelos que consideram a série univariada de log-retornos do portifólio versus mo- delos multivariados, que consideram as séries de log-retornos de cada ativo que compõe o portifólio e suas correlações condicionais. Além disso, são testados modelo propostos recentemente, que possuem pouca literatura a respeito, como o PS-GARCH e o VARMA-GARCH. Também propomos um novo modelo, que utiliza o resultado acumulado do portifólio nos últimos dias como variável exógena. Os diferentes modelos são avaliados em termos de sua adequação às exigëncias do Acordo de Basileia e seu impacto financeiro, em um período que inclui épocas de alta volatilidade. De forma geral, não foram notadas grandes diferenças de performance entre modelos univariados e multivariados. Os modelos mais complexos mostraram-se mais eficientes, produzindo resultados satisfatórios inclusive em tempos de crise. / The present work consists of a comparative study of several portfolio Value-at-Risk models. Univariate models, which consider only the portfolio log-returns series, are compared to multivariate models, which consider the log-returns series of each asset individually and their conditional correlations. Additionally, recently proposed models such as PS-GARCH and VARMA-GARCH are tested. We also propose a new model that uses past cumulative returns as exogenous variables. All models are evaluated in terms of their compliance to Basel Accord and financial impact, in period that includes high volatility times. In general, univariate and multivariate models performed similarly. More complex models yielded more accurate results, with satisfactory performance including in crisis periods.

Made available in DSpace on 2016-03-15T19:30:39Z (GMT). No. of bitstreams: 1 Luiz Guilherme Azevedo Mauad.pdf: 2910298 bytes, checksum: 249a2bed427bd7a8dc926ab2d3586459 (MD5) Previous issue date: 2010-07-01 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Purchasing high quality and low price products has become a consumer fixation, mainly where the lowest price is demanded and in reverses auctions, whether electronic or not. The importance of establishing retail prices of projects, products and services has been increasing. Therefore, it has become a strategic and challenging task for managers while also being one of their great fears. In a global and highly competitive market, price setting may influence consumers buying choices: a product s value and quality, which meet their expectations, will sell a product or project. On the other hand, a price inaccurately fixed may turn offers down and lead a company into unwished results. Research shows that markup pricing method is still the most common technique used by companies. However, fixing a price based on this method and taking into account a deterministic cost value may lead a company into making the wrong decisions and taking unnecessary risks. Prices undergo the influence of several costs and market related factors, which, somehow, have some kind of uncertainty risk. Nevertheless, when one is dealing with costs this uncertainty becomes more latent. Therefore, they must be taken into consideration in the company s pricing process. The present research study, based on RiskMetrics concepts such as VaR and, mainly, CorporateMetrics, proposes and applies a pricing model named Cost at Risk based Price (PCeR) in a high technology venture. The model approaches costs incurred stochastically instead of deterministically and takes into account the risks inherent to their composing parameters. The model has proven to be a useful and flexible tool, which offers to managers greater understanding when fixing retail prices. That understanding may assist organizations to reach a market, overcome their competitors and grow profitably. / Adquirir produtos com qualidade e preços baixos tornou-se uma obsessão para o consumidor,principalmente, nas concorrências em que o menor preço é exigido e nos leilões reversos,realizados por meio eletrônico ou não. A fixação de preços de venda para projetos, produtos e/ou serviços adquire, a cada dia, maior importância. Torna-se uma atividade estratégica e um dos grandes desafios para os gestores e, porque não dizer, um dos seus grandes temores. Em um mercado global e altamente competitivo, o dimensionamento de preço pode influir na decisão de compra do consumidor: o estabelecimento de valor e qualidade que atendam à sua expectativa favorece a venda do produto, ou projeto, já um preço mal dimensionado pode fazê-lo refugar ofertas e levar a empresa a resultados indesejados. Estudos mostram que a precificação custo acrescido , ainda hoje, é a técnica mais utilizada pelas empresas, para cumprir essa função. Porém, definir o preço, com base neste modelo e considerar apenas um valor de custo determinístico, poderá levar a empresa a decisões errôneas e riscos desnecessários. Sabe-se que o preço sofre influência de uma série de fatores ligados ao custo e ao mercado que, de certa forma, contêm certo grau de incerteza, porém é nos custos que estas incertezas tornam-se mais latentes. Então, não se pode deixar de considerá-las no processo de precificação da empresa. Este trabalho, baseado nos conceitos propostos pelo RiskMetrics, como o VaR e, principalmente, nas CorporateMetrics, propõe e aplica, em uma empresa de alta tecnologia, um modelo de precificação denominado Preço baseado no Custo em Risco (PCeR), que aborda os custos incorridos não mais de maneira determinística, mas de forma estocástica, levando em consideração os riscos inerentes aos parâmetros que o compõem. O modelo mostrou ser uma ferramenta útil e flexível aos gestores, oferecendo uma maior visibilidade na definição do preço de venda, visibilidade essa que pode levar a organização a conquistar mercado, superar a concorrência e crescer com lucratividade.

Made available in DSpace on 2010-04-20T20:14:59Z (GMT). No. of bitstreams: 0 Previous issue date: 1998-02-13T00:00:00Z / Apresenta o método value at risk (VaR) para se mensurar o risco de mercado, sob diferentes abordagens. Analisa a série histórica do índice Bovespa no período de 1995 a 1996 por meio de testes econométricos de normalidade, autocorrelação dos retornos e raiz unitária. Comparo valor obtido a partir dos diferentes modelos de estimação de volatilidade propostos e verifica qual dos modelos foi o mais adequado para o caso estudado. / The purpose of this dissertation is to compare the performance of three methods of volatility estimating used for value at risk models: an exponentially weighted moving average (RiskMetrics TM), GARCH (Generalized Autoregressive Conditional Heteroscedasticity) and TARCH (Threshold model). Concerning the latter, we decided to test it, given that GARCH models cannot properly capture the leverage etTect (negative shocks have a larger impact on volatility than positive shocks). The sample covers the daily São Paulo Stock Exchange index from 2 January 1995 to 30 December 1996. The test results indicated that the alternative models did not outperform RiskMetrics™ under the particular market conditions observed in the time period studied. Despite the fact that TARCH model can cope with negative or positive skewness, this model did not provide better results than RiskMetrics™. It seems to be reasonable not to attempt to make any general statement that one method is undoubtedly superior to another, given that test results may depend on the data period employed.

<p>SAMMANDRAG</p><p>Historisk Simulation, Delta-Normal och RiskMetrics prestation utvärderas med hjälp av Kupiecs Backtest. Value at Risk (VaR) beräknas med tre olika konfidensnivåer utifrån Affärsvärldens Generalindex och HSBC kopparindex. Utifrån överträdelser från verkligt utfall undersöks vilken VaR-modell som estimerar marknadsrisken bäst. VaR-modellernas prestation jämförs, och i analysen utreds hur konfidensnivå och tillgångars egenskaper påverkar VaR-modellernas prestation. Resultaten visar att Historisk Simulation presterar bättre än Delta-Normal och RiskMetrics på den högsta konfidensnivån vilket troligtvis beror på att RiskMetrics och Delta-Normal antar normalfördelning. RiskMetrics och Delta-Normal presterar dock bättre än Historisk Simulation på den lägsta konfidensnivån vilket sannolikt är en följd av att Historisk Simulation anpassar sig långsammare till volatilitetsförändringar. Undersökningen tyder även på att avtagningsfaktorn som RiskMetrics använder får minskad effekt vid högre konfidensnivåer varför skillnaden mellan Delta-Normals och RiskMetrics prestation är marginell på dessa nivåer.</p>