Value-at-Risk (VaR) is among financial institutions a commonly used tool for measuring market risk. Several methods to calculate VaR exists and different implementations often results in different VaR forecasts. An interesting implementation is historical simulation, and the purpose of this thesis is to examine whether historical simulation with dynamic volatility updating is useful as a model to calculate VaR and how this differs in regard to type of asset or instrument. To carry out the investigation six different models are implemented, which then are tested for statistical accuracy through Christoffersens test. We find that incorporation of volatility updating into the historical simulation method in many cases improves the model. The model also generates good results compared to other commonly used models, especially if the volatility is predicted through a GARCH(1,1) updating scheme. / Value-at-Risk (VaR) är ett bland finansiella institutioner vanligt mått för att mäta marknadsrisk. Det finns ett flertal olika sätt att beräkna VaR, vilka ofta ger olika resultat beroende på förutsättningar. Ett av dessa är historisk simulering, och syftet med denna uppsats är att undersöka huruvida historisk simulering med dynamiskt uppdaterande volatilitet är en användbar modell för beräkning av VaR och hur dess lämplighet beror på valt tillgångsslag eller instrument. För att besvara detta implementeras sex olika modeller för beräkning av VaR, vilka sedan testas med hjälp av Christoffersens test. Vi finner att inkorporering av dynamisk volatilitet i historisk simulering i många fall medför en förbättring av modellen ifråga om statistisk riktighet. Vidare kan historisk simulering med dynamiskt uppdaterande volatilitet anses vara konkurrenskraftig i jämförelse med andra vanligt använda modeller, framförallt då volatiliteten skattas genom GARCH(1,1).

The purpose of this thesis is to examine whether Swedish Equity L/S hedge funds present a lower market risk than the index S&P Europe 350 over our holding period using a GARCH/EGARCH Value-at-Risk model. The sample consists of 96 monthly observa- tions between March 2004 and February 2012. The examination shows that the hedge funds in general hold a lower market risk than the index for the next holding period and al- so present a lower estimated loss if our VaR loss is exceeded. This implies that hedge funds would be a good choice for investors to have in a portfolio to reduce the risk.

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<p>Value-at-Risk (VaR) is among financial institutions a commonly used tool for measuring market risk. Several methods to calculate VaR exists and different implementations often results in different VaR forecasts. An interesting implementation is historical simulation, and the purpose of this thesis is to examine whether historical simulation with dynamic volatility updating is useful as a model to calculate VaR and how this differs in regard to type of asset or instrument. To carry out the investigation six different models are implemented, which then are tested for statistical accuracy through Christoffersens test. We find that incorporation of volatility updating into the historical simulation method in many cases improves the model. The model also generates good results compared to other commonly used models, especially if the volatility is predicted through a GARCH(1,1) updating scheme.</p> / <p>Value-at-Risk (VaR) är ett bland finansiella institutioner vanligt mått för att mäta marknadsrisk. Det finns ett flertal olika sätt att beräkna VaR, vilka ofta ger olika resultat beroende på förutsättningar. Ett av dessa är historisk simulering, och syftet med denna uppsats är att undersöka huruvida historisk simulering med dynamiskt uppdaterande volatilitet är en användbar modell för beräkning av VaR och hur dess lämplighet beror på valt tillgångsslag eller instrument. För att besvara detta implementeras sex olika modeller för beräkning av VaR, vilka sedan testas med hjälp av Christoffersens test. Vi finner att inkorporering av dynamisk volatilitet i historisk simulering i många fall medför en förbättring av modellen ifråga om statistisk riktighet. Vidare kan historisk simulering med dynamiskt uppdaterande volatilitet anses vara konkurrenskraftig i jämförelse med andra vanligt använda modeller, framförallt då volatiliteten skattas genom GARCH(1,1).</p>

The diploma thesis "Value at Risk: Historical simulation, variance covariance method and Monte Carlo" aims to value the risk which real bond portfolio bears. The thesis is decomposed into two major chapters: Theoretical and Practical chapters. The first one speaks about VaR and conditional VaR theory including their advantages and disadvantages. Moreover, there are described three basic methods to calculate VaR and CVaR with adjustments to each method in order to increase the reliability of results. The last chapter brings results of VaR and CVaR computation. Many graphs, tables and images are added to the result section in order to make the outputs more visible and well-arranged.

The 2007 financial crisis highlighted the severe risks posed by counterparty defaults in financial markets. Assessing and addressing counterparty credit risk has consequently been a focal point of new regulations introduced in the wake of the crisis. The Central Clearing Counterparty (CCP) is at the heart of the solution, an entity dedicated to managing and mitigating counterparty risk in a market. CPPs manage risk by collecting collateral, referred to as margin, from the participants trading on the market. Appropriately sizing the margin is of utmost importance for the CCP to maintain the integrity of its operation and, by extension, protect the participants in the market. Most contemporary margin methodologies require significant resources which precludes frequent margin updates. In light of this issue, our work examines the capability of replicating the popular margin methodology Historical Simulation Value at Risk using machine-learning-based methods envisioning that an adequate such model could be used as a complement to the traditional model, providing real-time margin estimations. The experiment concerns portfolios containing stocks, bonds, and options and uses static market data and scenarios. We conclude that neither of the ensemble methods are sufficiently accurate, while both of the neural network-based models show moderate promise, warranting further development.

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 goal of the paper is to compare impacts of interest rate risk measuring meth-ods on capital requirements. The first section identifies methods for measuring interest rate risk and capital requirements for interest rate risk set by regulators. The second section compares capital requirements of model portfolio calculated by using standardized methods as well as internal models.

The diploma thesis Risks of using VaR models for portfolio management is focused on estimation of the portfolio VaR using basic and modified methods. The goal of this thesis is to point out some weakness of the basic methods and to demonstrate the estimation of VaR using improved methods to overcome these problems. The analysis will be perform theoretically and in practice. Only market risk will be the subject of the study. Several simulation and parametric methods will be introduced.

This paper explores the potential of historical simulation games to nurture historical consciousness. Merging the subject of history and game studies, the material analyzed is the digital game Crusader Kings 2 as well as player created narratives spawned from it. The paper uses a mixed method from game study and history didactics, and theories of historical consciousness to interpret the material. The study shows that the potential to develop historical consciousness do exist in the historical simulation game, and that the narratives that players create from play contain signs of historical consciousness. The study opens up the field for future case studies where the development of historical consciousness through historical simulation can be tested in a formal school setting. / Denna studie undersöker potentialen hos historiska simulationer i digitala spel att utveckla historiemedvetande. Ämnet historia och spelstudier blandas i denna uppsats där det digitala spelet Crusader Kings 2 och tillhörande spelarskapade narrativ undersöks. Studien använder en blandad metod från spelstudier och historiedidaktik. Teorier om historiemedvetande används för att tolka materialet. Undersökningen visar att det finns potential för detta historiska simulationsspel att utveckla historiemedvetande. Den visar även att tecken på historiemedvetande syns i de spelarskapade narrativen. Studien öppnar upp för framtida fallstudier där utvecklingen av historiemedvetande genom historisk simulation kan testas i formell skolmiljö.