MAYORGA, Rodrigo de Oliveira. An application of value at risk and expected shortfall / Rodrigo de Oliveira Mayorga. - 2016. 60f. Tese (Doutorado) - Universidade Federal do Ceará, Programa de Pós Graduação em Economia, CAEN, Fortaleza, 2016. / Submitted by Mônica Correia Aquino (monicacorreiaaquino@gmail.com) on 2017-06-07T18:33:28Z No. of bitstreams: 1 2016_tese_romayorga.pdf: 23551041 bytes, checksum: c9a78d3b82daf878118fea8674fe02e8 (MD5) / Approved for entry into archive by Mônica Correia Aquino (monicacorreiaaquino@gmail.com) on 2017-06-07T18:33:45Z (GMT) No. of bitstreams: 1 2016_tese_romayorga.pdf: 23551041 bytes, checksum: c9a78d3b82daf878118fea8674fe02e8 (MD5) / Made available in DSpace on 2017-06-07T18:33:45Z (GMT). No. of bitstreams: 1 2016_tese_romayorga.pdf: 23551041 bytes, checksum: c9a78d3b82daf878118fea8674fe02e8 (MD5) Previous issue date: 2016 / The last two decades have been characterized by significant volatilities in financial world marked by few major crises, market crashes and bankruptcies of large corporations and liquidations of major financial institutions. In this context, this study considers the Extreme Value Theory (EVT), which provides well established statistical models for the computation of extreme risk measures like the Value at Risk (VaR) and Expected Shortfall (ES) and examines how EVT can be used to model tail risk measures and related confidence interval, applying it to daily log-returns on four market indices. These market indices represent the countries with greater commercial trade with Brazil for last decade (China, U.S. and Argentina). We calculate the daily VaR and ES for the returns of IBOV, SPX, SHCOMP and MERVAL stock markets from January 2nd 2004 to September 8th 2014, combining the EVT with GARCH models. Results show that EVT can be useful for assessing the size of extreme events and that it can be applied to financial market return series. We also verified that MERVAL is the stock market that is most exposed to extreme losses, followed by the IBOV. The least exposed to daily extreme variations are SPX and SHCOMP. / As duas últimas décadas têm sido caracterizadas por volatilidades significativas no mundo financeiro em grandes crises, quebras de mercado e falências de grandes corporações e liquidações de grandes instituições financeiras. Neste contexto, este estudo considera a evolução da Teoria do Valor Extremo (EVT), que proporciona modelos estatísticos bem estabelecidos para o cálculo de medidas de risco extremos, como o Value at Risk (VaR) e Espected Shortfall (ES) e examina como a EVT pode ser usada para modelar medidas de risco raros, estabelecendo intervalos de confiança, aplicando-a aos log-retornos diários a quatro índices de mercado. Estes mercados representam os países com maior intercâmbio comercial com o Brasil (China, U.S. e Argentina). Calculamos o VaR e ES diários dos índices IBOV, SPX, SHCOMP e MERVAL, com dados diários entre de 02 de janeiro de 2004 e 08 de setembro de 2014, combinando a EVT com modelos GARCH. Os resultados mostram que EVT pode ser útil para avaliar o tamanho de eventos extremos e que ele pode ser aplicado a séries de retorno do mercado financeiro. Verifica-se ainda que MERVAL é o mercado de ações que está mais exposta a perdas extremas, seguido do IBOV. Os menos expostos a variações extremas diárias são SPX e SHCOMP.

With the ripples in the financial markets and economic stresses that occur around the world today, it would be beneficial to have some insight into the tools that help investors learn about the riskiness of their portfolios. At what value is one's portfolio in danger of being completely wiped out? We aim to further the understanding of values such as these and give an assessment of some risk measures by investing in an interactive portfolio, as well as estimating the values at risk and expected shortfalls of this portfolio.

With the ripples in the financial markets and economic stresses that occur around the world today, it would be beneficial to have some insight into the tools that help investors learn about the riskiness of their portfolios. At what value is one's portfolio in danger of being completely wiped out? We aim to further the understanding of values such as these and give an assessment of some risk measures by investing in an interactive portfolio, as well as estimating the values at risk and expected shortfalls of this portfolio.

Submitted by Sara Ribeiro (sara.ribeiro@ucb.br) on 2017-08-17T14:48:23Z No. of bitstreams: 1 LeonardoNascimentoCastroDissertacao2017.pdf: 1765989 bytes, checksum: fb4cfd563d11e2aa428d7c5af632c835 (MD5) / Approved for entry into archive by Sara Ribeiro (sara.ribeiro@ucb.br) on 2017-08-17T14:50:34Z (GMT) No. of bitstreams: 1 LeonardoNascimentoCastroDissertacao2017.pdf: 1765989 bytes, checksum: fb4cfd563d11e2aa428d7c5af632c835 (MD5) / Made available in DSpace on 2017-08-17T14:50:34Z (GMT). No. of bitstreams: 1 LeonardoNascimentoCastroDissertacao2017.pdf: 1765989 bytes, checksum: fb4cfd563d11e2aa428d7c5af632c835 (MD5) Previous issue date: 2017-01-01 / Due to the Crisis of 2008, the Basel Committee accelerated the process for update the Accord and identified some weaknesses such as the inability of V aR to capture the tail risk. Subsequently, it was recommended to substitute V aR, a non-coherent measure of risk due to the absence of subadditivity, by CV aR. However, in 2011 the absence of elicitability for CV aR was shown and this has led some people to believe that it is impossible to perform a backtesting for this risk measure. Elicitability is an mathematical property for model selection and not for validation, although the convexity of its scoring function is required for backtesting. It is important to know the identifiability and testability, which have a relation with elicitability. For a good backtesting in the Trading Book, the testable function must be sharp, which is strictly increasing and decreasing with respect to the predictive and realized variables, respectively, and meet the requirement of ridge backtest, which depends on the least possible V aR. The CV aR, while not being testable or elicitable, is at least conditionally elicitable and therefore also conditionally testable. To validate the CV aR models, simulations were made with the three Acerbi methods, two of this study for testing and another adapted from the quantile approximation. Of these six, none were perfect, but two presented better results than the V aR Backtesting. This study analyzed the risk measures V aR and CV aR by the Historical Simulation, Delta-Normal, Correlated Normal, Monte Carlo and Quasi-Monte Carlo Simulation methods in the 95%, 97.5% and 99% for the Brazilian bond and stock portfolios, as well as the Brazilian Real against the Dollar, Euro and Yen currencies, and used some backtesting for the two measures. This study also proposed a method to improve Backtesting results of V aR. / Devido ?? Crise de 2008 o Comit?? de Basileia acelerou o processo para atualiza????o do Acordo e identificou algumas falhas como, por exemplo, a incapacidade do V aR em captar o risco de cauda. Posteriormente, recomendou-se substituir o V aR, uma medida n??o coerente de risco devido ?? aus??ncia de subaditividade, pelo CV aR. Entretanto, em 2011 foi mostrada a aus??ncia da elicitabilidade para o CV aR e isso induziu algumas pessoas a pensarem ser imposs??vel realizar um backtesting para esta medida de risco. A elicitabilidade ?? uma propriedade matem??tica para a sele????o de modelo e n??o para a valida????o, apesar de que a convexidade de sua fun????o scoring ?? necess??ria para o backtesting. Foram introduzidos os conceitos de identificabilidade e testabilidade, que possuem uma rela????o com a elicitabilidade. Para um bom backtesting no Trading Book, a fun????o test??vel deve ser n??tida, que ?? estritamente crescente e decrescente em rela????o ??s vari??veis preditiva e realizada, respectivamente, e atender o requisito de ridge backtest, que dependa o m??nimo poss??vel do V aR. O CV aR, apesar de n??o ser elicit??vel nem test??vel, ?? pelo menos condicionalmente elicit??vel e, portanto, tamb??m condicionalmente test??vel. Para validar os modelos do CV aR, foram feitas simula????es com os tr??s m??todos de Acerbi, dois desta pesquisa para teste e outro adaptado da Aproxima????o dos N??veis de V aR. Destes seis, nenhum foi perfeito, mas dois apresentaram resultados melhores que o Backtesting do V aR. Esta pesquisa analisou as medidas de risco V aR e CV aR pelos m??todos Simula????o Hist??rica, Delta-Normal, Normal Correlacionado, Simula????o Monte Carlo e Quase-Monte Carlo nos intervalos de confian??a de 95%, 97,5% e 99% para as carteiras de t??tulos e a????es brasileiras, al??m das cota????es do Real frente ??s moedas D??lar, Euro e Iene, e utilizou alguns testes de ader??ncia para as duas medidas. Esta pesquisa tamb??m prop??s um m??todo para melhorar os resultados do Backtesting do V aR.

This thesis aims at implementing and evaluating the performance of multivariate Expected Shortfall models on high frequency foreign exchange data. The implementation is conducted with a unique portfolio consisting of five foreign exchange rates; EUR/SEK, EUR/NOK, EUR/USD, USD/SEK and USD/NOK. High frequency is in this context defined as observations with time intervals from second by second up to minute by minute. The thesis consists of three main parts. In the first part, the exchange rates are modelled individually with time series models for returns and realized volatility. In the second part, the dependence between the exchange rates is modelled with copulas. In the third part, Expected Shortfall is calculated, the risk contribution of each exchange rate is derived and the models are backtested. The results of the thesis indicate that three of the five final models can be rejected at a 5% significance level if the risk is measured by Expected Shortfall (ES0:05). The two models that cannot be rejected are based on the Clayton and Student’s t copulas, the only two copulas with heavy left tails. The rejected models are based on the Gaussian, Gumbel-Hougaard and Frank copulas. The fact that some of the copula models are rejected emphasizes the importance of choosing an appropriate dependence structure. The risk contribution calculations show that the risk contributions are highest from EUR/NOK and USD/NOK, and that EUR/USD has the lowest risk contribution and even decreases the portfolio risk in some cases. Regarding the underlying models, it is concluded that for the data used in this thesis, the final combined time series and copula models perform quite well, given that the purpose is to measure the risk. However, the most important parts to capture seem to be the fluctuations in the volatilities as well as the tail dependencies between the exchange rates. Thus, the predictions of the return mean values play a less significant role, even though they still improve the results and are necessary in order to proceed with other parts of the modelling. As future research, we first and foremost recommend including the liquidity aspect in the models. / Syftet med denna masteruppsats är att implementera och utvärdera multidimensionella Expected Shortfall-modeller på högfrekvent växelkursdata. Implementeringen och utvärderingen utförs med en unik portfölj bestående av fem växelkurser; EUR/SEK, EUR/NOK, EUR/USD, USD/SEK och USD/NOK. Högfrekventa observationer är i denna uppsats definierade som sekundvisa upp till minutvisa observationer. Uppsatsen består av tre huvuddelar. I den första delen modelleras växelkurserna individuellt med tidsseriemodeller för växelkursförändringarna i form av avkastning och realiserad volatilitet. I del två modelleras beroendestrukturerna mellan de olika växelkurserna med hjälp av copulas. I den tredje och sista delen beräknas Expected Shortfall och riskbidragen från de enskilda växelkurserna, varefter modellerna utfallstestas. De slutgiltiga resultaten indikerar att tre av de fem föreslagna modellerna kan förkastas vid en signifikansnivå på 5% om risken mäts med Expected Shortfall (ES0:05). De två modeller som inte kan förkastas är baserade på Clayton och Student’s t copulas, vilka särskiljer sig från övriga copulas genom att de har tjocka vänstersvansar. De modeller som förkastas är baserade på Gaussian, Gumbel-Hougaard och Frank copulas. Det faktum att några copula-modeller förkastas betonar vikten av att välja en lämplig beroendestruktur. Riskbidragsberäkningarna visar att EUR/NOK och USD/NOK bidrar mest till den totala risken i portföljen och att EUR/USD har det lägsta riskbidraget, där EUR/USD till och med minskar risken i vissa fall. Vad gäller underliggande modeller så visas det att för den tillgängliga datan i den här uppsatsen så fungerar tidsseriemodeller i kombination med copulas bra, givet att syftet är att mäta risk. Dock tyder resultaten på att volatilitetsfluktuationer samt svansberoenden mellan växelkurserna är de mest väsentliga delarna att fånga. Väntevärdesprognoserna för avkastningarna har mindre inverkan på de slutgiltiga beräkningarna, även om de fortfarande förbättrar resultaten och i sig är nödvändiga för fortsatt modellering. För framtida studier rekommenderar vi först och främst att inkludera likviditetsaspekter i modellerna.

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.

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.