Dissertação (mestrado)—Universidade de Brasília, Instituto de Ciências Exatas, Departamento de Estatística, 2015. / Submitted by Fernanda Percia França (fernandafranca@bce.unb.br) on 2016-03-22T19:46:38Z No. of bitstreams: 1 2015_YuriSampaioMaluf.pdf: 4291479 bytes, checksum: 4a9954a7905294836d257652f0ce1753 (MD5) / Approved for entry into archive by Marília Freitas(marilia@bce.unb.br) on 2016-05-26T16:30:44Z (GMT) No. of bitstreams: 1 2015_YuriSampaioMaluf.pdf: 4291479 bytes, checksum: 4a9954a7905294836d257652f0ce1753 (MD5) / Made available in DSpace on 2016-05-26T16:30:44Z (GMT). No. of bitstreams: 1 2015_YuriSampaioMaluf.pdf: 4291479 bytes, checksum: 4a9954a7905294836d257652f0ce1753 (MD5) / Neste trabalho, estudamos a formulação da distribuição de funções de variáveis aleatórias contínuas dependentes. O mecanismo de modelagem da dependência é feita via funções cópulas. Dentre os resultados obtidos formulamos a expressão geral da distribuição da soma de n variáveis aleatórias dependentes. Expandimos a abordagem para a distribuição de outras funções de variáveis aleatórias tais como o quociente, produto e uma combinação convexa. Por meio das R-Vines Cópulas, obtivermos também a expressão da soma de n variáveis aleatórias em que cada componente é governada por um processo GARCH. A partir deste resultado, calculamos o Value-at-Risk (VaR) e Expected Shortfalls (ES) da soma dessas variáveis. Em função desta estrutura, as medidas de risco passam a adquirir um comportamento dinâmico. Ao final do trabalho exibimos algumas ilustrações numéricas via simulação de Monte Carlo. Apresentamos também uma aplicação com dados reais provenientes de bolsas de valores da América Latina. / In this thesis, we studied the distribution of function of dependents continuous random variables. The modeling dependencies structures are made via copula functions. We obtain the general expression of the distribution of the sum of n dependents random variables. This approach is expanded for other functions such as ratio, product and a convex combination. Using R-Vines Copulas, we also derive an expression of the sum of n dependents random variables, being each component governed by AR-GARCH process. From these results, we assess the Value-at-Risk (VaR) and Expected Shortfalls (ES) of the sum of these variables. According to this structure, the VaR takes a dynamic behavior. At the end of this thesis, we show some numerical illustrations via Monte Carlo simulation. An application with real data from Latin American stock markets is also presented.

Examensarbetet studerar möjligheterna att använda en statisk cross hedge för att prissäkra etanol. Situationen som analyseras är hämtad från Lantmännen Agroetanol. Agroetanol är Sveriges största producent av etanol och driver den första anläggning i Sverige där vete omvandlas till etanol. Anläggningen är Sveriges största och byggs för närvarande ut så att kapaciteten kommer under år 2008 kommer att öka med 300 procent. Priset på spannmål har stigit dramatiskt under år 2007 samtidigt som etanolpriset har sjunkit något. Mot bakgrund av dessa båda negativa prisrörelser utvärderas hedging med hjälp finansiella instrument som en möjlighet för Agroetanol att skydda sin produktion. Genom att använda futurekontrakt, med socker som underliggande tillgång, kan Agroetanol minska sin marknadsrisk. Efter en analys av Lantmännens befintliga riskmått i form av stresstest, konstateras att Lantmännen bör överväg att använda sig av Expected Shortfall för att mäta koncernens marknadsrisk. Expected Shortfall bygger på det mycket populära Value at Risk, men uppvisar ytterligare några fler positiva egenskaper. Vi rekommenderar att Lantmännenkoncernen använder sig av Expected Shortfall i arbetet med att kvantifiera sin finansiella marknadsrisk inom samtliga affärsområden och bolag. På detta sätt kan riskerna associerade med varje verksamhet enkelt analyseras. Slutligen kan den metodik för cross hedging som presenteras i examensarbetet användas i flera olika sammanhang och problemställningen är inte unik för groetanol. Författarna hoppas på detta sätt att undersökningen kan fungera som en vägledning även vid andra liknande projekt. / This master thesis studies the application of a static cross hedge when hedging ethanol. The case studied has been provided by Lantmännen Agroetanol, operator of the largest ethanol plant in Sweden. The plant produce ethanol from grain and the capacity is currently being expanded by 300 percent. Changes in the price of both grain and ethanol have been dramatic during 2007, with a decrease in the price of ethanol and a sharp increase in the price of wheat. These changes both have a negative impact on the operations of Agroetanol and this thesis look to hedging with futures as a method to lessen the exposure to price changes. Using future contracts derived on sugar prices we conclude that Agroetanol can decrease its market risk. An analysis of the methods for measuring financial risks at Lantmännen concludes that the use of Expected Shortfall, a measurement derived from Value at Risk, have a number of advantages. We therefore recommend that this measure is implemented throughout the corporation providing a consistent measure of financial risks. This enables every part of the organization to be analyzed based on its contribution to the total risk exposure. Finally the method used in the thesis can be used in a number of situations and the difficulties observed at Agroetanol are by no means unique. We hope that this study can provide an example for studies that aim to solve similar difficulties.

<p>Examensarbetet studerar möjligheterna att använda en statisk cross hedge för att prissäkra etanol. Situationen som analyseras är hämtad från Lantmännen Agroetanol. Agroetanol är Sveriges största producent av etanol och driver den första anläggning i Sverige där vete omvandlas till etanol. Anläggningen är Sveriges största och byggs för närvarande ut så att kapaciteten kommer under år 2008 kommer att öka med 300 procent. Priset på spannmål har stigit dramatiskt under år 2007 samtidigt som etanolpriset har sjunkit något. Mot bakgrund av dessa båda negativa prisrörelser utvärderas hedging med hjälp finansiella instrument som en möjlighet för Agroetanol att skydda sin produktion.</p><p>Genom att använda futurekontrakt, med socker som underliggande tillgång, kan Agroetanol minska sin marknadsrisk. Efter en analys av Lantmännens befintliga riskmått i form av stresstest, konstateras att Lantmännen bör överväg att använda sig av Expected Shortfall för att mäta koncernens marknadsrisk. Expected Shortfall bygger på det mycket populära Value at Risk, men uppvisar ytterligare några fler positiva egenskaper. Vi rekommenderar att Lantmännenkoncernen använder sig av Expected Shortfall i arbetet med att kvantifiera sin finansiella marknadsrisk inom samtliga affärsområden och bolag. På detta sätt kan riskerna</p><p>associerade med varje verksamhet enkelt analyseras. Slutligen kan den metodik för cross hedging som presenteras i examensarbetet användas i</p><p>flera olika sammanhang och problemställningen är inte unik för groetanol. Författarna hoppas på detta sätt att undersökningen kan fungera som en vägledning även vid andra liknande projekt.</p> / <p>This master thesis studies the application of a static cross hedge when hedging ethanol. The case studied has been provided by Lantmännen Agroetanol, operator of the largest ethanol plant in Sweden. The plant produce ethanol from grain and the capacity is currently being expanded by 300 percent. Changes in the price of both grain and ethanol have been dramatic during 2007, with a decrease in the price of ethanol and a sharp increase in the price of wheat. These changes both have a negative impact on the operations of Agroetanol and this thesis look to hedging with futures as a method to lessen the exposure to price changes.</p><p>Using future contracts derived on sugar prices we conclude that Agroetanol can decrease its market risk. An analysis of the methods for measuring financial risks at Lantmännen concludes that the use of Expected Shortfall, a measurement derived from Value at Risk, have a number of advantages. We therefore recommend that this measure is implemented throughout the corporation providing a consistent measure of financial risks. This enables every part of the organization to be analyzed based on its contribution to the total risk exposure.</p><p>Finally the method used in the thesis can be used in a number of situations and the difficulties observed at Agroetanol are by no means unique. We hope that this study can provide an example for studies that aim to solve similar difficulties.</p>

Risk measurement tools and strategies have until recently been calibrated for a low-for-long interest rate environment. However, in the current higher interest rate environment, banking supervisory entities have intensified their regulatory pressure on institutions to enhance their assessment and monitoring of interest rate risk and credit spread risk. The European Banking Authority (EBA) has released updated guidelines on the assessment and monitoring of Credit Spread Risk in the Banking Book (CSRBB), which will replace the current guidelines by 31st December 2023. The new guidelines identify the CSRBB as a separate risk category apart from Interest Rate Risk in the Banking Book (IRRBB), and specifies the inclusion of liabilities in therisk calculations. This paper proposes a CSRBB model that conforms to the updated EBA guidelines. The model uses a historical simulation Value at Risk (HSVaR) and Expected Shortfall (ES) approach, and includes a 90-day holding period, as suggested by Finansinspektionen (FI). To assess the effectiveness of the model, it is compared with a standardised model of FI, and subjected to backtesting. Additionally, the paper suggests modifications to the model to obtain more conservative results. / Riskmätningsverktyg och strategier har sedan nyligen anpassats till en lågräntemiljö. Dock till följd av den nuvarande högre räntemiljön har tillsynsmyndigheter för bankväsendet satt ökat tryck på institutioners utvärdering och rapportering av ränterisk och kreditspreadrisk. Den Europeiska Bankmyndigheten (EBA) har publicerat uppdaterade riktlinjer för bedömning och rapportering av kreditspreadsrisken i bankboken (CSRBB), som ersätter de nuvarande riktlinjerna den 31 december 2023. De nya riktlinjerna identifierar CSRBB som en separat riskkategori från ränterisk i bankboken (IRRBB) och specificerar inkluderingen av skulder i riskberäkningarna. Denna uppsats föreslår en CSRBB-modell som följer EBAs uppdaterade riktlinjer. Modellen använder en Value at Risk (VaR) metodik baserat på historiska simulationer och Expected Shortfall (ES), samt antar en 90-dagars innehavsperiod som föreslås av Finansinspektionen (FI). Modellens effektivitet utvärderas genom en jämförelse med FIs standardmodell för kreditspreadrisken i bankboken, samt genom backtesting. Slutligen diskuteras möjliga justeringar av modellen för att uppnå mer konservativa resultat.

The volatility model approach to forecasting Value at Risk is complemented with modelling of Expected Shortfalls using an extreme value approach. Using three models from the GARCH family (GARCH, EGARCH and GJR-GARCH) and assuming two conditional distributions, normal Gaussian and Student t’s distribution, to make predictions of VaR, the forecasts are used as a threshold for assigning losses to the distribution tail. The Expected Shortfalls are estimated assuming that the violations of VaR follow the Generalized Pareto distribution, and the estimates are evaluated. The results indicate that the most efficient model for making predictions of VaR is the asymmetric GJR-GARCH, and that assuming the t distribution generates conservative forecasts. In conclusion there is evidence that the commodities are characterized by asymmetry and conditional normality. Since no comparison is made, the EVT approach can not be deemed to be either superior or inferior to standard approaches to Expected Shortfall modeling, although the data intensity of the method suggest that a standard approach may be preferable.

The focus of this thesis is on the employment of theoretical and practical quantile methods in addressing prediction, risk measurement and inference problems. From a prediction perspective, a problem of creating model-free prediction intervals for a future unobserved value of a random variable drawn from a sample distribution is considered. With the objective of reducing prediction coverage error, two common distribution transformation methods based on the normal and exponential distributions are presented and they are theoretically demonstrated to attain exact and error-free prediction intervals respectively. The second problem studied is that of estimation of expected shortfall via kernel smoothing. The goal here is to introduce methods that will reduce the estimation bias of expected shortfall. To this end, several one-step bias correction expected shortfall estimators are presented and investigated via simulation studies and compared with one-step estimators. The third problem is that of constructing simultaneous confidence bands for quantile regression functions when the predictor variables are constrained within a region is considered. In this context, a method is introduced that makes use of the asymmetric Laplace errors in conjunction with a simulation based algorithm to create confidence bands for quantile and interquantile regression functions. Furthermore, the simulation approach is extended to an ordinary least square framework to build simultaneous bands for quantiles functions of the classical regression model when the model errors are normally distributed and when this assumption is not fulfilled. Finally, attention is directed towards the construction of prediction intervals for realised volatility exploiting an alternative volatility estimator based on the difference of two extreme quantiles. The proposed approach makes use of AR-GARCH procedure in order to model time series of intraday quantiles and forecast intraday returns predictive distribution. Moreover, two simple adaptations of an existing model are also presented.

This study employs Extreme Value Theory and several univariate methods to compare their Value-at-Risk and Expected Shortfall predictive performance. We conduct several out-of-sample backtesting procedures, such as uncondi- tional coverage, independence and conditional coverage tests. The dataset in- cludes five different stock markets, PX50 (Prague, Czech Republic), BIST100 (Istanbul, Turkey), ATHEX (Athens, Greece), PSI20 (Lisbon, Portugal) and IBEX35 (Madrid, Spain). These markets have different financial histories and data span over twenty years. We analyze the global financial crisis period sep- arately to inspect the performance of these methods during the high volatility period. Our results support the most common findings that Extreme Value Theory is one of the most appropriate risk measurement tools. In addition, we find that GARCH family of methods, after accounting for asymmetry and fat tail phenomena, can be equally useful and sometimes even better than Extreme Value Theory based method in terms of risk estimation. Keywords Extreme Value Theory, Value-at-Risk, Expected Shortfall, Out-of-Sample Backtesting Author's e-mail ozturkdurmus@windowslive.com Supervisor's e-mail ies.avdulaj@gmail.com

In order to evaluate and manage portfolio risk, we separated this project into three sections. In the first section we constructed a portfolio with 15 different stocks and six options with different strategies. The portfolio was implemented in Interactive Brokers and rebalanced weekly through five holding periods. In the second section we modeled the loss distribution of the whole portfolio with normal and student-t distributions, we computed the Value-at-Risk and expected shortfall in detail for the portfolio loss in each holding week, and then we evaluated differences between the normal and student-t distributions. In the third section we applied the ARMA(1,1)-GARCH(1,1) model to simulate our assets and compared the polynomial tails with Gaussian and t-distribution innovations.

This report is for MA575: Market and Credit Risk Models and Management, given by Professor Marcel Blais. In this project, three different methods for estimating Value at Risk (VaR) and Expected Shortfall (ES) are used, examined, and compared to gain insightful information about the strength and weakness of each method. In the first part of this project, a portfolio of underlying assets and vanilla options were formed in an Interactive Broker paper trading account. Value at Risk was calculated and updated weekly to measure the risk of the entire portfolio. In the second part of this project, Value at Risk was calculated using semi-parametric model. Then the weekly losses of the stock portfolio and the daily losses of the entire portfolio were both fitted into ARMA(1,1)-GARCH(1,1), and the estimated parameters were used to find their conditional value at risks (CVaR) and the conditional expected shortfalls (CES).

In order to evaluate and manage portfolio risk, we separated this project into three sections. In the first section we constructed a portfolio with 15 different stocks and six options with different strategies. The portfolio was implemented in Interactive Brokers and rebalanced weekly through five holding periods. In the second section we modeled the loss distribution of the whole portfolio with normal and student-t distributions, we computed the Value-at-Risk and expected shortfall in detail for the portfolio loss in each holding week, and then we evaluated differences between the normal and student-t distributions. In the third section we applied the ARMA(1,1)-GARCH(1,1) model to simulate our assets and compared the polynomial tails with Gaussian and t-distribution innovations.