Value-at-Risk (VaR) model fails to predict financial risk accurately especially during financial crises. This is mainly due to the model’s inability to calibrate new market information and the fact that the risk measure is characterised by poor tail risk quantification. An alternative approach which comprises of the Expected Shortfall measure and the Lognormal Jump-Diffusion (LJD) model has been developed to address the aforementioned shortcomings of VaR. This model is called the Simulated-Expected-Shortfall (SES) model. The Maximum Likelihood Estimation (MLE) approach is used in determining the parameters of the LJD model since it’s more reliable and authenticable when compared to other nonconventional parameters estimation approaches mentioned in other literature studies. These parameters are then plugged into the LJD model, which is simulated multiple times in generating the new loss dataset used in the developed model. This SES model is statistically conservative when compared to peers which means it’s more reliable in predicting financial risk especially during a financial crisis. / Statistics / M.Sc. (Statistics)

The role of risk management has gained momentum in recent years most notably after the recent financial crisis. This thesis uses a quantitative approach to evaluate the theory of value at risk which is considered a benchmark to measure financial risk. The thesis makes use of both parametric and non parametric approaches to evaluate the effectiveness of VAR as a standard tool in measuring risk of stock portfolio. This study uses the normal distribution, student t-distribution, historical simulation and the exponential weighted moving average at 95% and 99% confidence levels on the stock returns of Sonny Ericsson, Three Months Swedish Treasury bill (STB3M) and Nordea Bank. The evaluations of the VAR models are based on the Kupiec (1995) Test. From a general perspective, the results of the study indicate that VAR as a proxy of risk measurement has some imprecision in its estimates. However, this imprecision is not all the same for all the approaches. The results indicate that models which assume normality of return distribution display poor performance at both confidence levels than models which assume fatter tails or have leptokurtic characteristics. Another finding from the study which may be interesting is the fact that during the period of high volatility such as the financial crisis of 2008, the imprecision of VAR estimates increases. For the parametric approaches, the t-distribution VAR estimates were accurate at 95% confidence level, while normal distribution approach produced inaccurate estimates at 95% confidence level. However both approaches were unable to provide accurate estimates at 99% confidence level. For the non parametric approaches the exponentially weighted moving average outperformed the historical simulation approach at 95% confidence level, while at the 99% confidence level both approaches tend to perform equally. The results of this study thus question the reliability on VAR as a standard tool in measuring risk on stock portfolio. It also suggest that more research should be done to improve on the accuracy of VAR approaches, given that the role of risk management in today’s business environment is increasing ever than before. The study suggest VAR should be complemented with other risk measures such as Extreme value theory and stress testing, and that more than one back testing techniques should be used to test the accuracy of VAR.

Η πολύπλοκη μορφή που απέκτησαν οι χρηματοοικονομικές αγορές κατά τη διάρκεια των δύο τελευταίων δεκαετιών, είχε ως αποτέλεσμα την απώλεια πολύ υψηλών κεφαλαίων από τις επιχειρήσεις και από τις τράπεζες. Η ανάγκη για συστηματική μέτρηση του χρηματοοικονομικού κινδύνου οδήγησε στην επινόηση του μεγέθους της αξίας σε κίνδυνο (Value-at-Risk, VaR). Η μέθοδος αυτή παρέχει στον ενδιαφερόμενο έναν αριθμό που εκφράζει τη μέγιστη αναμενόμενη ζημία μίας επένδυσης για δεδομένη χρονική περίοδο και δεδομένο επίπεδο εμπιστοσύνης. Παρά το γεγονός ότι η VaR έχει κάποιους περιορισμούς που απαιτούν τη χρήση stress test και scenario test, συνολικά, η VaR είναι η καλύτερη ανεξάρτητη τεχνική μέτρησης των κινδύνων που είναι διαθέσιμη. Στόχος της παρούσας διπλωματικής εργασίας είναι η μέτρηση της VaR ενός χαρτοφυλακίου. Επιπλέον, μέσα από αυτήν την εργασία θα γίνει κατανοητό τι είναι η VaR, πώς μπορεί να υπολογιστεί, ποια είναι τα κύρια χαρακτηριστικά της και ποια είναι τα πλεονεκτήματα και τα μειονεκτήματά της. Τέλος, ιδιαίτερη έμφαση δίνεται στην παρουσίαση των μεθόδων υπολογισμού της VaR. / The inextricable form of the financial markets during the last two decades result in the loss of high capital from the businesses and banks. The need of a systemic measurement of the financial risk leads to the invention of the Value-at-Risk method. This method provides the interested person with a number which expresses the potential maximum loss of an investment for a given period of time and a given confidence level. Despite the fact that VaR has some restrictions demanding the use of stress test and scenario test, altogether, VaR is the best independent measuring technique of the risks that it is available. The aim of this dissertation is to measure the VaR of a portfolio. Moreover, it will be registered what VaR is, how it can be measured, which are its main characteristics, its advantages and disadvantages. Lastly, more emphasis is given to the presentation of the measuring methods of VaR.

Magistro darbe nagrinėjamas šiuo metu vienas moderniausių rizikos matų – rizikos vertė (angl.Value-at-risk) Analizuojami trys pagrindiniai VaR rodiklio skaičiavimo metodai: variacijos/kovariacijos, istorinio modeliavimo ir Monte Karlo simuliacijos keliamų prielaidų, sudėtingumo ir adekvatumo požiūriais. Visų trijų metodų pagalba dabartinėmis rinkos sąlygomis atliekami empiriniai tyrimai, siekiant įvertinti rizikos vertes valiutų ir akcijų rinkose, atlikta gautų rizikos verčių palyginamoji analizė bei patikrintas naudotų metodų tikslumas. Autorės suformuluota hipotezė, kad VaR rodiklio skaičiavimo metodai nėra tinkami naudoti pereinamuoju laikotarpiu kuomet ekonominė aplinka ir padėtis nėra stabili iš dalies patvirtinta, nes atliktų tyrimų rezultatai atmetė tik variacijos/kovariacijos bei istorinio modeliavimo metodų tinkamumą. / In this master‘s work analyzed one of the modern risk measurements – Value-at-Risk (VaR). The paper examined three main VaR calculation methods: variance/covariance, historical simulation and Monte Carlo generations satisfying in the terms of the assumptions, adequacy and complexity. For all three methods was carried out empirical studies to assess the risk of currency and stock markets, made comparative analysis of the obtained risk values and verified accuracy of used methods in the current market conditions. The authors formulated the hypothesis that the VaR indicator calculation methods are not suitable for use during the transitional period when the economic environment and situation is not stable partially confirmed because the results of tests performed to reject just the variance / covariance and historical simulation methods.

The thesis describes commonly used measures of risk, such as volatility, Value at Risk (VaR) and Expected Shortfall (ES), and is tasked with creating models for measuring market risk. It is concerned with the risk over daily and over monthly horizons and shows the shortcomings of a square-root-of-time approach for converting VaR and ES between horizons. Parametric models, geometric Brownian motion (GBM) and GARCH process, and non-parametric models, historical simulation (HS) and some its possible improvements, are presented. The application of these mentioned models is demonstrated using real data. The accuracy of VaR models is proved through backtesting and the results are discussed. Part of this thesis is also a simulation study, which reveals the precision of VaR and ES estimates.

Submitted by Fabiola Costa (famedina06@hotmail.com) on 2010-08-24T14:18:56Z No. of bitstreams: 1 Dissertacao_Fabiola_Medina_Costa.pdf: 981365 bytes, checksum: 368c8b3a6a54c3a8e7c0f62130bcf2a3 (MD5) / Approved for entry into archive by Vitor Souza(vitor.souza@fgv.br) on 2010-08-24T14:39:21Z (GMT) No. of bitstreams: 1 Dissertacao_Fabiola_Medina_Costa.pdf: 981365 bytes, checksum: 368c8b3a6a54c3a8e7c0f62130bcf2a3 (MD5) / Made available in DSpace on 2010-08-24T17:42:48Z (GMT). No. of bitstreams: 1 Dissertacao_Fabiola_Medina_Costa.pdf: 981365 bytes, checksum: 368c8b3a6a54c3a8e7c0f62130bcf2a3 (MD5) Previous issue date: 2010-05-28 / This paper proposes the historical simulation model to calculate the VaR, considering return ajusted by the realized volatility measured from intraday returns. The database consists of five most liquid share among the different segments of Bovespa Index. For the proposed methodology we used two of the empirical theories of the empirical literature - adjusted historical simulation and realized volatility. The Kupiec tes and Christoffersen test are used to analized and veryfy the proposed methodology performance. / O presente trabalho propõe para o cálculo VaR o modelo de simulação histórica, com os retornos atualizados pela volatilidade realizada calculada a partir de dados intradiários. A base de dados consiste de cinco ações entre as mais líquidas do Ibovespa de distintos segmentos. Para a metodologia proposta utilizamos duas teorias da literatura empírica – simulação histórica ajustada e volatilidade realizada. Para análise e verificação do desempenho da metodologia proposta utilizamos o Teste de Kupiec e o Teste de Christoffersen.

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Atenciosamente, Secretaria de Registro, Suzi on 2011-09-16T18:56:44Z (GMT) / Submitted by Sheyla Brito (sheyla.brito@yahoo.com) on 2011-09-19T15:05:46Z No. of bitstreams: 1 Dissertacao_Sheyla-Brito_versao-final_2011-09.pdf: 903173 bytes, checksum: 2e19043be0af3ce4c63641a374093018 (MD5) / Approved for entry into archive by Suzinei Teles Garcia Garcia (suzinei.garcia@fgv.br) on 2011-09-19T15:12:27Z (GMT) No. of bitstreams: 1 Dissertacao_Sheyla-Brito_versao-final_2011-09.pdf: 903173 bytes, checksum: 2e19043be0af3ce4c63641a374093018 (MD5) / Approved for entry into archive by Suzinei Teles Garcia Garcia (suzinei.garcia@fgv.br) on 2011-09-19T15:12:47Z (GMT) No. of bitstreams: 1 Dissertacao_Sheyla-Brito_versao-final_2011-09.pdf: 903173 bytes, checksum: 2e19043be0af3ce4c63641a374093018 (MD5) / Made available in DSpace on 2011-09-19T15:15:25Z (GMT). No. of bitstreams: 1 Dissertacao_Sheyla-Brito_versao-final_2011-09.pdf: 903173 bytes, checksum: 2e19043be0af3ce4c63641a374093018 (MD5) Previous issue date: 2011-08-19 / This dissertation is focused on studying the Brazilian stock market behavior, more specifically related to a pair trading strategy. The assets included in here come from listed stocks of Brazilian Stock Exchange Index (Ibovespa) and the pair selection is exclusively based on a statistic characteristics, known as cointegration, without fundamentalist analysis. The applied theory treats similar movement of stock prices between pairs which tends to revert to an equilibrium mean of price differences. The strategy will present positive returns when reversion occurs in a pre-defined time. Back-testing data comprises intraday prices from 2006 until 2010 of Ibovespa stocks. The tools in which pair selection and trading rules are coded are MATLAB (selection) and Streambase (trading). Selection is processed through Dickey-Fuller augmented test into MATLAB to check the existence of a unit root on an error time series of a linear combination of stock prices, for each pair. Operation is simulated through intraday back-testing data as mentioned, input into Streambase tool. Within back-testing period, the strategy results are profitable in 2006, 2007 and 2010. Parameters, to enter and stop the operation, were adjusted for the first month of 2006 and could be successfully applied for the whole year of 2006 (yield of Selic + 5.8% for 2006), for 2007, where yield were close to Selic and for 2010, with yield of Selic + 10.8%. In periods of high volatility (2008 and 2009), tests with the same parameters of the ones adjusted for 2006 generated losses, showing the strategy is highly impacted per volatility returns of stock prices. This behavior suggests that, in actual operations, parameters should be constantly reevaluated in order to adapt them to volatile scenarios. / Esta dissertação estuda o movimento do mercado acionário brasileiro com o objetivo de testar a trajetória de preços de pares de ações, aplicada à estratégia de pair trading. Os ativos estudados compreendem as ações que compõem o Ibovespa e a seleção dos pares é feita de forma unicamente estatística através da característica de cointegração entre ativos, sem análise fundamentalista na escolha. A teoria aqui aplicada trata do movimento similar de preços de pares de ações que evoluem de forma a retornar para o equilíbrio. Esta evolução é medida pela diferença instantânea dos preços comparada à média histórica. A estratégia apresenta resultados positivos quando a reversão à média se efetiva, num intervalo de tempo pré-determinado. Os dados utilizados englobam os anos de 2006 a 2010, com preços intra-diários para as ações do Ibovespa. As ferramentas utilizadas para seleção dos pares e simulação de operação no mercado foram MATLAB (seleção) e Streambase (operação). A seleção foi feita através do Teste de Dickey-Fuller aumentado aplicado no MATLAB para verificar a existência da raiz unitária dos resíduos da combinação linear entre os preços das ações que compõem cada par. A operação foi feita através de back-testing com os dados intra-diários mencionados. Dentro do intervalo testado, a estratégia mostrou-se rentável para os anos de 2006, 2007 e 2010 (com retornos acima da Selic). Os parâmetros calibrados para o primeiro mês de 2006 puderam ser aplicados com sucesso para o restante do intervalo (retorno de Selic + 5,8% no ano de 2006), para 2007, onde o retorno foi bastante próximo da Selic e para 2010, com retorno de Selic + 10,8%. Nos anos de maior volatilidade (2008 e 2009), os testes com os mesmos parâmetros de 2006 apresentaram perdas, mostrando que a estratégia é fortemente impactada pela volatilidade dos retornos dos preços das ações. Este comportamento sugere que, numa operação real, os parâmetros devem ser calibrados periodicamente, com o objetivo de adaptá-los aos cenários mais voláteis.

Diploma thesis Business risks in insurance and their quantification describes the business risks to which insurance companies are exposed in their activities. Thesis is focused on market risk and quantification of market risk in insurance companies. It includes determination of the specifications for the activities of insurance companies, regulation and characteric of business risks in insurance. Large part of the thesis deals with the method of Value at Risk as a tool to measure market risk as well as individual methods to calculate it. In the conclusion, thesis describes the processes of quantification of market risk in Generali PPF Holding and in Česká poisťovňa, which gives a practical insight into the issues of market risk in insurance companies.

The importance of sound financial risk management has become increasingly emphasised in recent years, especially with the financial crisis of 2007-08. The Basel Committee sets the international standards and regulations for banks and financial institutions, and in particular under market risk, they prescribe the internal application of the measure Value-at-Risk. However, the most established non-parametric Value-at-Risk model, historical simulation, has been criticised for some of its unrealistic assumptions. This thesis investigates alternative approaches for estimating non-parametric Value-at-Risk, by examining and comparing the capability of three counterbalancing weighting methodologies for historical simulation: an exponentially decreasing time weighting approach, a volatility updating method and, lastly, a more general weighting approach that enables the specification of central moments of a return distribution. With real financial data, the models are evaluated from a performance based perspective, in terms of accuracy and capital efficiency, but also in terms of their regulatory suitability, with a particular focus on the Swedish market. The empirical study shows that the capability of historical simulation is improved significantly, from both performance perspectives, by the implementation of a weighting methodology. Furthermore, the results predominantly indicate that the volatility updating model with a 500-day historical observation window is the most adequate weighting methodology, in all incorporated aspects. The findings of this paper offer significant input both to existing research on Value-at-Risk as well as to the quality of the internal market risk management of banks and financial institutions. / Betydelsen av sund finansiell riskhantering har blivit alltmer betonad på senare år, i synnerhet i och med finanskrisen 2007-08. Baselkommittén fastställer internationella normer och regler för banker och finansiella institutioner, och särskilt under marknadsrisk föreskriver de intern tillämpning av måttet Value-at-Risk. Däremot har den mest etablerade icke-parametriska Value-at-Risk-modellen, historisk simulering, kritiserats för några av dess orealistiska antaganden. Denna avhandling undersöker alternativa metoder för att beräkna icke-parametrisk Value-at‑Risk, genom att granska och jämföra prestationsförmågan hos tre motverkande viktningsmetoder för historisk simulering: en exponentiellt avtagande tidsviktningsteknik, en volatilitetsuppdateringsmetod, och slutligen ett mer generellt tillvägagångssätt för viktning som möjliggör specifikation av en avkastningsfördelnings centralmoment. Modellerna utvärderas med verklig finansiell data ur ett prestationsbaserat perspektiv, utifrån precision och kapitaleffektivitet, men också med avseende på deras lämplighet i förhållande till existerande regelverk, med särskilt fokus på den svenska marknaden. Den empiriska studien visar att prestandan hos historisk simulering förbättras avsevärt, från båda prestationsperspektiven, genom införandet av en viktningsmetod. Dessutom pekar resultaten i huvudsak på att volatilitetsuppdateringsmodellen med ett 500 dagars observationsfönster är den mest användbara viktningsmetoden i alla berörda aspekter. Slutsatserna i denna uppsats bidrar i väsentlig grad både till befintlig forskning om Value-at-Risk, liksom till kvaliteten på bankers och finansiella institutioners interna hantering av marknadsrisk.

The financial crisis of 2007-2008 highlighted the societal impacts of bank risk-taking. A strong focus on maximizing profits for shareholders combined with a disregard for, and  underestimation of risks led to the downfall of large banks such as Lehman Brothers and multiple other banks getting bailed out by several governments and other banks. The financial crisis spread and impacted all major financial markets across the globe, which highlights the importance of investigating the banking sector from a global perspective. In addition, the influences of corporate social responsibility (CSR) on financial performance and risk have been a growing topic in research as well as in practice. Most banks today invest large amounts of money in CSR activities. The question of how bank spending in CSR activities impacts market risk is important. There are two contradicting views on CSR activities and market risk. The risk mitigation view suggests that banks that focus on stakeholder satisfaction have lower risk due to increased moral capital with stakeholders. The overinvestment view suggests that managers waste scarce resources by overinvesting in CSR activities to further selfish goals and therefore increase risk. This study examines the relationship between sustainability performance (ESG Combined score) and market risk (VaR/CVaR) using a deductive approach. The authors sample 159 banks from 39 countries and all 7 economic regions from 2011-2022. Data is used for testing hypotheses. Results find high ESG Combined Scores are associated with lower VaR/CVaR and results are robust to modifications in VaR/CVaR calculation assumptions. Disaggregation of ESG pillars shows that social pillar scores decrease VaR/CVaR in banks while environmental and governance pillars are insignificant. Results primarily lend support to the risk mitigation view and stakeholder theory stating that firms should focus more on stakeholder satisfaction than maximizing shareholder value. Complementing theories such as legitimacy theory and resources-based view are also considered important theories for explaining the results.