Dissertations / Theses on the topic 'Valle at risk'

2014 - 2015
Basel accords define the capital requirements for banks. There are three types of risk on which is based the calculation of this requirement: operational risk, i.e. the risk of losses related to potential inefficiencies of the system of control of the bank, the market risk, i.e. the risk related to any eventual leakage of the securities portfolio (of the institute or belonging to a single customer) determined by the market and credit risk, i.e. the risk incurred by the banks for any inability partial or total of the counterparty to fulfill the obligation assumed. The three risks defined within the Basel Agreement, define the three cornerstones of the activity of banking advice. The main responsibility of each operator banking, resides in the ability to perceive and anticipate the risks of positions in acquisition and on which the Institute will expose, evaluating the acceptability by defining appropriate actions to be taken. The need to measure and adequately control the risks taken by a bank is felt particularly in investment activity and trading of securities, which is exposed to the volatility of prices of assets exchanged. For institutions which take speculative positions in currencies, bonds or shares, there is in fact a real possibility that the losses associated with a single position broke, within a short time interval, the profits made in the course of months. In the first part of the work is analyzed the typology of risk indicated with the term "market risk". More precisely, with the term market risk is the risk of changes in the market value of an instrument or of a portfolio of financial instruments linked to unexpected changes in market conditions. One of the indicators is widely used to measure the market risk of active and follow him in his temporal evolution is the VaR (Value at Risk) that can be defined as the "…maximum loss in which an investor may incur, with a predetermined level of probability α, for a time horizon future N+H". If ζ N = ( r1...Rn) are available information at the time n, the VaR will be a function of ζ N , α, h by synthesizing VaR N (h; α) with h=1,2…and 0 < a <1. The VaR is essentially a synthetic index that measure the market risk of the 3 active or portfolio analysis. The financial risks relate to unexpected changes and unfavorable market value of certain financial positions because it is not certain whether the issuer will be able or not to fulfill its obligations (coupon or capital). On the same conceptual basis defines the credit risk, understood as the risk of default of the counterparty in a financial contract for medium long term. The second chapter is dedicated to the analysis of models for the assessment of credit risk appeared in recent years and mainly used so far by the banks. In the literature were developed three different approaches to describe the credit risk: structural approach, a reduced form and to incomplete information. The third chapter echoing what indicated in the first part of the work is based on the examination of the fundamental principles of the protection of the customer in the provision of advice to the investment. Studies of behavioral finance that investigate the choices of asset allocation financial show that these are affected particularly by two elements: the capacity to take risks and the attitude to risk to investors. Investment firms, thanks to the MiFID Directive, have the obligation of profiling customers through a questionnaire to ensure their protection and protection against risks arising from financial investments. Aspects investigated by the MiFID questionnaires are compared with the elements that, according to the literature, influences the choices of individual investment. In confirmation of what is required by the MiFID Directive, are extracted from a sample of customers made available by a Banca di Credito Cooperativo Bell, a representative for each category of risk on which the securities portfolio is applied a model VaR aimed to verify the degree of risk related to Portfolio proposed as a result of the consultancy activities carried out .The choices of asset allocation undertaken by individuals are often addressed by investment firms which, through a questionnaire, collect personal information from the subjects to recommend investments in line with their needs and characteristics. For portfolio management services or consultancy service, investment firms shall submit the subject to the test of adequacy and, in the case in which I do not answer to certain requirements, 4 they will be precluded the investment in financial instruments risky. Consequently, the decisions of asset allocation financial does not always arise from an individual choice made by the investor but are often addressed by a person competent to allow the customer the attainment of its objectives. However, many studies demonstrate the impact of certain aspects of the profile of the investors in their propensity to risk and consequently in the choices of allocation of assets. The analysis has allowed us to compare the aspects that according to the literature influence the risk propensity of investors with what is required in the phase of practical placement of the product. In the daily advice, tools made available are mainly focused on the aspects linked to the capacity of taking risks, then on the study of the investment objectives and the elucidation of theholding period. As regards the risk tolerance literature amply investigates the influence of socio demographic and personal, that are not always considered to be at the basis of the risk assessment in the questionnaires MiFID. The fundamental variables, confirmed in literature at the end of the definition of a proper risk profile of the counterparty, are the consistency of the income and wealth of the respondent. Are collected information with regard to the profession and the bachgraud risk borne by investors, elements considered capable of influencing choices of asset allocation. The study title knowledge in the field of investments and the experience gained in the financial aspects are considered influential at a theoretical level that are reflected in the questions asked to customers through the questionnaire. To support what is proposed, and signed by the customer, is estimated for the set data obtained, a model VaR applied to each single portfolio for the three customers identified. The period considered runs from 01/01/2016 to 16/09/2016. On the basis of the frequency of transactions are identified three representative positions of the three risk profiles defined in the process of profiling of the customer previously argued. Specifically: - Low risk : Position historically entered in the registers of the institute for a period exceeding 10 years. Employee private company. 5 Preparation of Upper Medium in financial activities. The total capital invested € 30,000 managed in n. 15 portfolio transactions thus distributed : 9 purchase transactions and 4 sales operations. The number of securities in the portfolio : n.2 _ Unicredit and Mediolanum. - Medium risk : Position entered by more than 5 years in the demographics of the isitituto.Public employee, profile financially diversified, are not present phenomena of concentration of capital in savings products inside of the institute or of third parties. Preparation Upper Medium in financial activities. The total capital invesstito 25,000 € managed in n. 36 portfolio transactions thus distributed : 16 purchase transactions and 20 sales operations. The number of securities in the portfolio: n.2 _, UNICREDIT and ENEL - High risk: Position entered from less than 5 years in the demographics of the Institute.Free professional expert in the financial sector, diversified profile, are not present phenomena of concentration of capital in savings products inside of the institute or of third parties. The total capital invested 80.000 € managed in n. 196 portfolio transactions thus distributed : 110 operations of purchase and 86 sales operations. Nuemro of securities in the portfolio : n.5 _ Mps, Saipem, Unicredit,Fincantieri,Ubi. In all three cases the pattern formulated with α = 5% is not infringed, in fact, on the basis of risk criteria and prudence defined by the Institute during placement and management of savings and the ratio between the actual violations of the model and the number of observations is maintained below the 5 % target. The same result is obtained as a result of an arbitrary remodulation of three portfolios considered, in fact, while modifying the compositions by reversing the titles between the same customers, the model retains its effectiveness while remaining in the margins of the 5% defined. A first reason can be found in the increasing diversification of the sector, namely a merch diversification of the portfolio on the basis of the nature of the title 6 (banking, energy, etc.) . In the case of low risk, in fact, with respect to the initial establishment of the portfolio is introduced the principle of diversification of the sector that allows the subject to reduce the concentration of capital in a same sector (see the banking systems in the specific case) and improve the values of risk. In the other two cases, on the contrary, is violated the component of sectoral diversification by increasing the concentration of the portfolio in bank shares thus obtaining a worsening of the riskiness of the model and an increase in violations of VaR. The estimation of the model has allowed us to validate the proposed and accepted by the customer, by dropping a tool typically used within the scope of financial corporate governance on private portfolios in order to confirm statistically as proposed within the consulting business. [edited by Author]
XIV n.s.

This thesis consists of three empirical essays on the Value-at-Risk (VaR) estimates. The first empirical study (Chapter 2) evaluates the performance of bank VaRs. The second empirical study (Chapter 3) investigates the predictive power of various VaR models using bank data. The third empirical study (Chapter 4) explores VaR estimates with high-frequency data. The first study examines the performance of VaR estimates at seven international banks from 2001 to 2012. Using statistical tests, we find that bank VaRs were conservatively estimated in pre-crisis and post-crisis periods. During financial crisis, while some banks continued to overstate their VaRs, the others significantly underestimated their risk. The potential causes of the poor performance of bank VaRs are also discussed. The second study investigates the predictive power of various VaR models using bank data. We find that the GARCH-based models are superior in estimating bank VaRs in both normal and crisis periods. We conclude that good VaR estimates at banks can be obtained using simple, accessible models rather than the complicated approach or banks’ internal model. Thus, we argue that VaR should not be blamed for misleading risk estimates during financial crisis. The third study evaluates VaR estimates using 5-minute sampling data of WTI Futures. First, we acknowledge the value of high-frequency data on the measure of volatility to characterize the quantile forecast of asset returns. Second, we find that quantile combination can improve the forecast accuracy. With the VaR implication, we show that VaR combination provides more accurate and robust results than individual VaR estimates.

The main focus of this thesis lies on description of Risk Management in context of Energy Trading. The paper will predominantly discuss Value at Risk and its modifications as a main overall indicator of Energy Risk.

The main idea of current PhD thesis is the analysis of bank value and risk interdependence, and that bank value is conected with bank activity riskiness on consistent pattern and that this dependency is advisable to measure on probability basis with simulation modeling. In the work are presented systemic view of risk, risk sorts, risk management including cash flow risk management and credit risk management, bank value and valuation methodology, modeling and use in practical tasks.
Disertacijoje nagrinėjamos banko vertės ir rizikos sąveikos problemos, ginama tezė, kad banko vertė susijusi su banko veiklos rizikų portfeliu dėsningai ir kad šią priklausomybę tikslinga matuoti per tikimybės ir patikimumo prizmes imitavimo būdu. Darbe pateikiamas susistemintas požiūris į riziką, jos rūšis, rizikos valdymą išskiriant pinigų srautų rizikos valdymą bei kredito rizikos val-dymą atskirai, bei į banko vertę ir banko vertinimo metodologiją, modeliavimą, jų taikymą praktikoje.

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Civil and Environmental Engineering, 2014.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 124-129).
This thesis addresses the question of how to maximize the value of energy capital projects in light of the various risks faced by these projects. The risks can be categorized as exogenous risks (not in control of involved entities) and endogenous risks (arising from sub-optimal decisions by involved entities). A dominant reason for poor project performance is the endogenous risks associated with weak incentives to deliver optimal project outcomes. A key objective of this research is to illustrate that risk-sharing through contracts is central to incentivize the involved entities to maximize overall project value. The thesis presents a risk management framework for energy capital projects that accounts for both exogenous risks and endogenous risks to evaluate the optimal risk management strategies. This work focuses on a carbon capture and storage project (CCS) with enhanced oil recovery (EOR). CCS is projected to play a key role in reducing the global CO₂ emissions. However, the actual deployment of CCS is likely to be lower than projected because of the various risks and uncertainties involved. The analysis of CCS-EOR projects presented in this thesis will help encourage the commercial deployment of CCS by identifying the optimal risk management strategies. This work analyzes the impact of the exogenous risks (market risks, geological uncertainty) on the value of the CCS-EOR project, and evaluates the optimal contingent decisions. Endogenous risks arise from the involvement of multiple entities in the CCS-EOR project; this thesis evaluates alternate CO₂ delivery contracts in terms of incentives offered to the individual entities to make the optimal contingent decisions. Key findings from this work illustrate that the final project value depends on both the evolution of exogenous risk factors and on the endogenous risks associated with response of the entities to change in the risk factors. The results demonstrate that contractual risk-sharing influences decision-making and thus affects project value. For example, weak risk-sharing such as in fixed price CO₂-EOR contracts leads to a high likelihood of sub-optimal decision-making, and the resulting losses can be large enough to affect investment and project continuity decisions. This work aims to inform decision-makers in capital projects of the importance of considering strong contractual risk-sharing structures as part of the risk management process to maximize project value.
by Anna Agarwal.
Ph. D.

When measuring market risk, credit institutions and Alternative Investment Fund Managers may deviate from equally weighting historical data in their Value-at-Risk calculation and instead use an exponential time series weighting. The use of expo-nential weighting in the Value-at-Risk calculation is very popular because it takes into account changes in market volatility (immediately) and can therefore quickly adapt to VaR. In less volatile market phases, this leads to a reduction in VaR and thus to lower own funds requirements for credit institutions. However, in the ex-ponential weighting a high volatility in the past is quickly forgotten and the VaR can be underestimated when using exponential weighting and the VaR may be un-derestimated. To prevent this, credit institutions or Alternative Investment Fund Managers are not completely free to choose a weighting (decay) factor. This article describes the legal requirements and deals with the calculation of the permissible weighting factor. As an example we use the exchange rate between Euro and Polish zloty to estimate the Value-at-Risk. We show the calculation of the weighting factor with two different approaches. This article also discusses exceptions to the general legal requirements.

The financial crisis of 2007/2008 brought about a debate concerning the quality of risk management models, such as Value at Risk (VaR) models. Several studies have tried to make conclusions about multiple VaR models in periods around the crisis. The conclusions differ, but the Extreme Value Theory (EVT) is considered to be a good prediction model in times of unstable financial markets.  In this thesis, the VaR for six financial instruments; the OMXS 30, the OMX Stockholm Financials PI, the OMX Stockholm Materials PI and the currencies USD/SEK, GBP/SEK and EUR/SEK are estimated with the Historical Simulation, the Monte Carlo Simulation and the Variance- Covariance Method, with a 95 percent confidence interval. The risk is estimated both for single instruments as well as portfolios in times before, during and after the crisis with the purpose of concluding which of the VaR models more accurately predict risk for specific instruments/portfolios in different time periods of the crisis.   No direct conclusions can be made about the accuracy of the models before, during or after the crisis. The only clear conclusion can be drawn for the single instruments regarding the EUR. All methods predict more accurate results for this instrument compared to the other instruments. The clearest conclusion for the portfolios is that portfolios holding larger weights of indexes show on larger VaR estimations. Also, the modified Monte Carlo Simulation and the Variance-Covariance Method estimate lower risk in general than the Historical Simulation.

The Financial Accounting Standards Board (FASB) and the Public Company Accounting Oversight Board (PCAOB) have proposed standards that could alter the judgments of users of financial statements. This study examines how certain regulations including revenue measurement choices made by management combined with risk disclosure as proposed by the PCAOB could interact with the propensity of the user to rely on financial information to affect how a class of private company financial statement users - seed equity investors - value a private company. Through experimental methods manipulating revenue measurement choice and risk disclosure, I find that seed equity investor value judgments of early stage companies are significantly influenced by accounting disclosures. Specifically, accounting disclosures regarding level of risk and revenue measurement that accompany financial models in the valuation process significantly alter a seed equity investor's value judgment of early stage companies. This segment of financial statement users tends to place the majority of their reliance on non-financial, subjective factors as predictors of future success of early stage companies. Further, their judgments are swayed by wholly different financial disclosures than their "Wall Street" investor counterparts in that conservative and low risk information creates large revisions in value judgment. The implication of this study is to suggest that "Main Street" investors consume financial information and their related disclosures differently than "Wall Street" investors - an inference important for standards setters to understand as they craft regulations that govern private companies.

The purpose of this thesis is to test the risk-measure Value-at-Riskand techniques for calculating it on data from the Financial Crisis of2007–2010. Different “pre-Financial Crisis” approaches to calculatingValue-at-Risk are considered, and tested on data from the period ofthe Financial Crisis. Also combinations of different approaches aretested.

Estimation of Value-at-Risk is done using the two different frame-works: Historical simulation (regular and the Hybrid approach) andparametric (conditional heteroscedastic) models.

The conditional heteroscedastic models considered are the EGARCHand the APARCH, calibrated using QMLE-methods. They are applied to the normal and Student’s t-distributions, Generalized ErrorDistribution and a non-parametric distribution. Consequently, a semi-parametric approach consisting of a non-parametric distribution alongwith an ARCH model is considered.

Quantile regression as by Koenker (1978) is used for the parameterestimation of the Historical simulation models used.

The Value-at Risk models are validated using Christoffersen’s con-ditional coverage test.Four stock indices (NIKKEI 225, NASDAQ 100, FTSE 100 andISEQ-overall) are evaluated, selected based on location and the re-gional effect of the Financial Crisis. Models are calibrated based ondata from before the Financial Crisis of 2007–2010, as the crisis isknown at present (April 2010).

It is found that the present approach to Value-at-Risk estimationcan not be considered redundant due to the extreme events of theFinancial Crisis.

Value at Risk (VaR) models have gained increasing momentum in recent years. Market VaR is an important issue for banks since its adoption as a primary risk metric in the Basel Accords and the requirement that it is calculated on a daily basis. Credit risk modelling has become increasingly important to banks since the advent of Basel 11 which allows banks with sophisticated modelling techniques to use internal models for the purpose of calculating capital requirements. A high level of credit risk is often the key reason behind banks failing or experiencing severe difficulty. Conditional Value at Risk (CVaR) measures extreme risk, and is gaining popularity with the recognition that high losses are often impacted by a small number of extreme events.

In this thesis we are interested in financial risk and the instrument we want to use is Value-at-Risk (VaR). VaR is the maximum loss over a given period of time at a given confidence level. Many definitions of VaR exist and some will be introduced throughout this thesis. There two main ways to measure risk and VaR: through volatility and through percentiles. Large volatility in financial returns implies greater probability of large losses, but also larger probability of large profits. Percentiles describe tail behaviour. The estimation of VaR is a complex task. It is important to know the main characteristics of financial data to choose the best model. The existing literature is very wide, maybe controversial, but helpful in drawing a picture of the problem. It is commonly recognised that financial data are characterised by heavy tails, time-varying volatility, asymmetric response to bad and good news, and skewness. Ignoring any of these features can lead to underestimating VaR with a possible ultimate consequence being the default of the protagonist (firm, bank or investor). In recent years, skewness has attracted special attention. An open problem is the detection and modelling of time-varying skewness. Is skewness constant or there is some significant variability which in turn can affect the estimation of VaR? This thesis aims to answer this question and to open the way to a new approach to model simultaneously time-varying volatility (conditional variance) and skewness. The new tools are modifications of the Generalised Lambda Distributions (GLDs). They are four-parameter distributions, which allow the first four moments to be modelled nearly independently: in particular we are interested in what we will call para-moments, i.e., mean, variance, skewness and kurtosis. The GLDs will be used in two different ways. Firstly, semi-parametrically, we consider a moving window to estimate the parameters and calculate the percentiles of the GLDs. Secondly, parametrically, we attempt to extend the GLDs to include time-varying dependence in the parameters. We used the local linear regression to estimate semi-parametrically conditional mean and conditional variance. The method is not efficient enough to capture all the dependence structure in the three indices —ASX 200, S&P 500 and FT 30—, however it provides an idea of the DGP underlying the process and helps choosing a good technique to model the data. We find that GLDs suggest that moments up to the fourth order do not always exist, there existence appears to vary over time. This is a very important finding, considering that past papers (see for example Bali et al., 2008; Hashmi and Tay, 2007; Lanne and Pentti, 2007) modelled time-varying skewness, implicitly assuming the existence of the third moment. However, the GLDs suggest that mean, variance, skewness and in general the conditional distribution vary over time, as already suggested by the existing literature. The GLDs give good results in estimating VaR on three real indices, ASX 200, S&P 500 and FT 30, with results very similar to the results provided by historical simulation.

CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO
A partir da década de 90, a metodologia Value at Risk (VaR) se difundiu pelo mundo, tanto em instituições financeiras quanto em não financeiras, como uma boa prática de mensuração de riscos. Em geral, abordagens paramétricas são muito utilizadas pelo mercado, apesar de freqüentemente não levarem em conta uma característica muito encontrada nas distribuições dos retornos de ativos financeiros: a presença de caudas pesadas. Uma abordagem baseada na Teoria dos Valores Extremos (TVE) é uma boa solução quando se deseja modelar caudas de distribuições probabilísticas que possuem tal característica. Em contra partida, poucos são os trabalhos que procuram desenvolver a TVE aplicada a ativos de renda-fixa. Com base nisto, este estudo propõe uma abordagem de simples implementação de cálculo de VaR para ativos de renda-fixa baseado na Teoria dos Valores Extremos.
Since the 90 decade, the use of Value at Risk (VaR) methodology has been disseminated among both financial and non-financial institutions around the world, as a good practice in terms of risks management. In spite of the fact that it does not take into account one of the most important characteristics of financial assets returns distribution - fat tails (excess of kurtosis), the parametric approach is the most used method for Value at Risk measurement. The Extreme Value Theory (EVT) is an alternative method that could be used to avoid the underestimation of Value at Risk, properly modeling the characteristics of probability distribution tails. However, there are few works that applied EVT to fixed-income market. Based on that, this study implements a simple approach to VaR calculation, in which the Extreme Value Theory is applied to fixed-income assets.

COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
A partir da década de 90, a metodologia de Valor em Risco (VaR) se difundiu pelo mundo, tanto em instituições financeiras quanto em não financeiras, como uma boa prática de mensuração de riscos. Um dos fatos estilizados mais pronunciados acerca das distribuições de retornos financeiros diz respeito à presença de caudas pesadas. Isso torna os modelos paramétricos tradicionais de cálculo de Valor em Risco (VaR) inadequados para a estimação de VaR de baixas probabilidades, dado que estes se baseiam na hipótese de normalidade para as distribuições dos retornos. Sendo assim, o objetivo do presente trabalho é investigar o desempenho de modelos baseados na Teoria dos Valores Extremos para o cálculo do VaR. Os resultados indicam que os modelos baseados na Teoria dos Valores Extremos são adequados para a modelagem das caudas, e consequentemente para a estimação de Valor em Risco quando os níveis de probabilidade de interesse são baixos.
Since the 90 decade, the use of Value at Risk (VaR) methodology has been disseminated among both financial and non-financial institutions around the world, as a good practice in terms of risks management. The existence of fat tails is one of the striking stylized facts of financial returns distributions. This fact makes the use of traditional parametric models for Value at Risk (VaR) estimation unsuitable for the estimation of low probability events. This is because traditional models are based on the conditional normality assumption for financial returns distributions. The main purpose of this dissertation is to investigate the performance of VaR models based on Extreme Value Theory. The results indicates that Extreme Value Theory based models are suitable for low probability VaR estimation.

This thesis proposes new approaches to Value-at-Risk estimation using (1) Multivariate GARCH Dynamic Conditional Correlation volatility model with skewed Student’s-t distributions, (2) Bayesian GARCH model with Student’s-t distribution, and (3) Bayesian Markov-Switching GJR-GARCH model with skewed Student’s-t distributions, incorporating copula functions and extreme value theory. A new approach for selecting a proper threshold in the Peaks Over Threshold method for extreme value theory analysis called the hybrid method is also proposed. The proposed Value-at-Risk models are compared to the traditional Value-at-Risk models commonly used by banks. Back-testing results following Kupiec (1995) unconditional coverage test, Christoffersen (1998) independent and conditional coverage test, Basel traffic light test, Santos and Alves (2012) new independent test, Dowd (2002) bootstrap back-test, and Engle and Manganelli (2004) Dynamic Quantile test show that Value-at-Risk models constructed following extreme value theory produced reliable Value-at-Risk estimates. Furthermore, Value-at-Risk models incorporating the hybrid method for threshold selection produced more stable Value-at-Risk estimates compared to the traditional Value-at-Risk models.

Usage of financial measurements that address the default probability of counterparties have been market practice for some time. Quantifying counterparty credit risk is usually done through the credit value adjustment which adjusts the value from a risk-free value to a risky value. When quantifying the credit value adjustment there is an important assumption that the financial exposure (value) and probability of counterparty default are independent variables. Wrong-way risk implies a relationship where exposure and probability of default are increasing together. It is an unfavourable relationship since as a party stands to gain more the probability of the counterparty not being able to pay also increase. When removing the independency assumption, the quantification of the credit value adjustment becomes more complex and there are several different methodologies with the aim to quantify CVA without the independency assumption. This paper analyses different methods of quantification and discusses different potential mitigators of wrong-way risk. But also, a case study searching for potential wrong-way exposures at a Swedish investment bank. The case study considers whether the exposures could potentially be influenced by wrong-way risk through stress tests on different value adjustments. The stress tests change the value adjustment and in turn imply wrong-way movements. At an investment bank that work towards minimizing risk it would be surprising to find large wrong-way risk exposures. But there are some interesting observations which could be deemed as wrong-way movements and would be interesting for the bank to investigate. Overall for the bank, wrong-way risk exposure cannot be claimed as significant. Conclusions involve modelling approach I deem the most useful in a perspective of calibration methodology, computer efficiency and deviation. Also, some suggestion of further development of this paper.
Under en tid har användning av finansiella mått som inkluderar motpartskreditrisk varit marknadsstandard. Kreditvärdesjustering används för att kvantifiera motpartskreditrisk och justerar värdet från ett riskfritt till ett värde som inkluderar motpartskreditrisk. När man justerar värdet används ett viktigt antagande som säger att den finansiella exponeringen (värdet) samt sannolikheten att motparten inte uppfyller sina förpliktelser är oberoende variabler. Felvägsrisk implicerar ett förhållande där exponeringen och sannolikheten att motparten inte kan uppfylla sina förpliktelser ökar tillsammans. Det är ett ofördelaktigt förhållande eftersom när en part kan tjäna mer ökar sannolikheten att motparten inte kan betala. När oberoende-antagandet tas bort blir kvantifieringen mer komplex, men det finns flera olika metoder som kvantifierar kreditvärdesjusteringen utan oberoende-antagandet. Denna uppsats analyserar olika kvantifieringsmetoder och diskuterar olika metoder för att minimera felvägsrisk. Uppsatsen innehåller även en fältstudie med syfte att hitta felvägsrisk bland exponeringarna hos en svensk investeringsbank. Fältstudien överväger huruvida exponeringarna eventuellt kan vara influerade av felvägsrisk genom att stressa olika mått för värdejustering. Stresstesterna påverkar värdejusteringen som i sin tur kan implicera felvägsrisk. Hos en svensk investeringsbank vars arbete involverar att minimera risk hade det varit förvånande att hitta stora exponeringar med felvägsrisk. Men det finns vissa observationer som tycks påvisa ofördelaktiga förhållanden som tyder på felvägsrisk. Dessa observationer skulle vara intressant för banken att se över utifrån den potentiella felvägsrisken. Överlag för banken kan jag inte påstå att exponeringen av felvägsrisk är signifikant. Slutsatserna involverar vilken modelleringsmetod som jag anser är mest användbar utifrån kalibrering, dataeffektivitet och potentiell avvikelse. Samt några förslag på vidare utveckling av denna rapport.

Since financial markets are considered risky, there is a need to have credible tools that can estimate these risks. For a Central Clearing Counterparty it is of utmost importance to conduct accurate estimations of its members’ risk exposures to deter-mine their margin requirements. We have together with the Nasdaq Risk Analytics Engineering team, which provides systems for clearing risk managers, initiated this project to investigate how Artificial Intelligence can be implemented to support daily risk calculations made today. We have focused on Neural Networks because of their ability to effectively process data, which is an important foundation for making risk predictions. We have constructed and trained three different Neural Networks, a Fully Connected Feedforward, a Convolutional, and a Gated Recurrent Unit Neural Network, with the aim to replicate the Value-at-Risk calculations made using the conventional method Filtered Historical Simulation. We have mainly evaluated the networks’ ability to replicate these computations, but also examined their computational time. We have seen that all networks have a good ability to learn and replicate Filtered Historical Simulation. In addition, the networks are much faster. However, we have encountered issues with the scale of the data, namely to learn large shifts in the size of Value-at-Risk. We have seen that the Convolutional net-work is significantly better than the other two at dealing with this issue. We are yet convinced, given the networks’ ability to replicate conventional risk computations and their short execution time, that there are potentials for supporting the process of risk management as of today.

Financial practitioners use models in order to price, hedge and measure risk. These models are reliant on assumptions and are prone to ”model risk”. Increased innovation in complex financial products has lead to increased risk exposure and has spurred research into understanding model risk and its underlying factors. This dissertation quantifies model risk inherent in Value-at-Risk (VaR) on a variety of portfolios comprised of European options written on the ALSI futures index across various maturities. The European options under consideration will be modelled using the Black-Scholes, Heston and Variance-Gamma models.

L’objet de cette thèse est d’analyser comment traiter le problème de renouvellement du parc en tenant compte de la durabilité, tout en se plaçant dans une perspective de gestion du risque. Cette thèse apporte une double contribution, au niveau de la politique de gestion du parc et à celui de la méthode utilisée pour appliquer cette politique. Au niveau de la politique, elle étudie l’effet de l’adoption de nouveaux véhicules, disposant d’une technologie de pointe, sur le risque et le coût escompté du système de gestion du parc. Au niveau méthodologique, cette thèse apporte trois contributions. Tout d’abord, elle comporte une étude de la nouvelle formulation du problème du parc en utilisant une programmation stochastique à deux étapes et à multiples étapes et une valeur à risque conditionnelle (CVaR), prenant ainsi en considération l’incertitude dans le processus de décision. En outre, elle élabore une formulation récursive de la CVaR, qui tient compte de la cohérence dans le temps, et elle examine ses propriétés de convergence, dans un cadre dynamique. Enfin, la thèse modélise l’impact sur le profit et le risque de l’utilisation des contrats à option sur le problème de remplacement du parc
The purpose of this thesis is to conduct an analysis of how the fleet replacement problem can be addressed from both sustainability and risk management perspectives, simultaneously. The contribution of this thesis has two components, in fleet management policy and in the method used to apply it. At a policy level, this thesis addresses the effect of adoption of new technological advanced vehicles on the risk and expected cost of the fleet management system. At a methodological level, this thesis presents three contributions: First, it studies the new formulation of the fleet problem by using a two stage and a multi stage stochastic programming and conditional value at risk (CVaR), which accounts for the uncertainty in the decision process. Second, it models a recursive formulation of CVaR, which takes into account the time consistency, and studies its convergence properties, in a dynamic setting. Third, it models the impact on profit and risk from using option contracts on the fleet replacement problem

A mensuração do risco de um investimento é uma das mais importantes etapas para a tomada de decisão de um investidor. Em virtude disto, este trabalho comparou três métodos de estimação (tradicional, através da analise univariada dos retornos do portfólio; cópulas estáticas e cópulas dinâmicas) de duas medidas de risco: Value at Risk (VaR) e Expected Shortfall (ES). Tais medidas foram estimadas para o portfólio composto pelos índices BOVESPA e S&P500 no período de janeiro de 1998 a maio de 2012. Para as modelagens univariadas, incluindo as marginais das cópulas, foram comparados os modelos GARCH e EGARCH. Para cada modelo univariado, utilizamos as cópulas Normal, t-Student, Gumbel rotacionada e Joe-Clayton simetrizada, com isso totalizando 36 modelos comparados. Nas comparações do VaR e ES foram utilizados, respectivamente, o teste de Chritoffersen e o teste de Mcneil e Frey. Os principais resultados encontrados foram a superioridade de modelos que supõem erros com distribuição t-Student, assim como a identificação de mudança no comportamento dos parâmetros dinâmicos nos períodos de crise.
Measuring the risk of an investment is one of the most important steps in an investor's decision-making. With this in light, this study compared three estimation methods (traditional; by univariate analysis of portfolio returns; dynamic copulas and static copulas), of two risk measurements: Value at Risk (VaR) and Expected Shortfall (ES). Such estimated measures are performed for a portfolio composed by the BOVESPA and S&P500 indexes, ranging from January 1998 to May 2012. For univariate modelling (including copulas marginals), the GARCH and EGARCH models were compared,. Regarding copulas, we use Normal, t-Student, rotated Gumbel and symmetric Joe-Clayton, leading to a total of 36 models being compared. For the comparison of VaR and ES were used, respectively, the Christoffersen test, and the Mcneil and Frey test. The main results found were the superiority of models assuming the t-Student distributed errors, as well as the identification of a change in the behaviour of dynamic parameters in periods of crisis.

In financial risk management it is essential to be able to model dependence in markets and portfolios in an accurate and efficient way. A high positive dependence between assets in a portfolio can be devastating, especially in times of crises, since losses will most likely occur at the same time in all assets for such a portfolio. The dependence is therefore directly linked to the risk of the portfolio. The risk can be estimated by several different risk measures, for example Value-at-Risk and Expected shortfall. This paper studies some different ways to measure risk and model dependence, both in a theoretical and empirical way. The main focus is on copulas, which is a way to model and construct complex dependencies. Copulas are a useful tool since it allows the user to separately specify the marginal distributions and then link them together with the copula. However, copulas can be quite complex to understand and it is not trivial to know which copula to use. An implemented copula model might give the user a "black-box" feeling and a severe model risk if the user trusts the model too much and is unaware of what is going. Another model would be to use the linear correlation which is also a way to measure dependence. This is an easier model and as such it is believed to be easier for all users to understand. However, linear correlation is only easy to understand in the case of elliptical distributions, and when we move away from this assumption (which is usually the case in financial data), some clear drawbacks and pitfalls become present. A third model, called historical simulation, uses the historical returns of the portfolio and estimate the risk on this data without making any parametric assumptions about the dependence. The dependence is assumed to be incorporated in the historical evolvement of the portfolio. This model is very easy and very popular, but it is more limited than the previous two models to the assumption that history will repeat itself and needs much more historical observations to yield good results. Here we face the risk that the market dynamics has changed when looking too far back in history. In this paper some different copula models are implemented and compared to the historical simulation approach by estimating risk with Value-at-Risk and Expected shortfall. The parameters of the copulas are also investigated under calm and stressed market periods. This information about the parameters is useful when performing stress tests. The empirical study indicates that it is difficult to distinguish the parameters between the stressed and calm market period. The overall conclusion is; which model to use depends on our beliefs about the future distribution. If we believe that the distribution is elliptical then a correlation model is good, if it is believed to have a complex dependence then the user should turn to a copula model, and if we can assume that history will repeat itself then historical simulation is advantageous.

The promising cryptocurrency Bitcoin has attracted a lot of attention recently, but the high volatility of the Bitcoin price has so far been a barrier to widespread adoption. Given the way Bitcoin transactions work, users will be exposed to exchange rate risk even for short intraday horizons. This paper analyzes this risk, and compares it to more traditional assets, namely Gold and the Euro/USD exchange rate. To do this we make use of the recent literature on market risk measures for ultra-high-frequency data to construct an intraday Value at Risk measurement. This IVaR is based on a Monte Carlo simulation, where a log-ACD-ARMA-EGARCH model is used to describe the price movements. The results clearly indicate that for the intradaily horizon, Bitcoin is far more risky than Gold and Euro, which may challenge the applicability of Bitcoin as a medium of transaction. However in our opinion this risk is not large enough to outweigh the potential benefits that Bitcoin offers.

Thesis (MBA)--Stellenbosch University, 2001.
ENGLISH ABSTRACT: Commercial banks, investment banks, insurance companies, non-financial firms, and pension funds hold portfolios of assets that may include stocks, bonds, currencies, and derivatives. Each institution needs to quantify the amount of risk its portfolio is exposed to in the course of a day, week, month, or year. Extreme events in financial markets, such as the stock market crash of October 1987, are central issues in finance and particularly in risk management and financial regulation. A method called value at risk (VaR) can be used to estimate market risk. Value at risk is a powerful measure of risk that is gaining wide acceptance amongst institutions for the management of market risk. Value at Risk is an estimate of the largest lost that a portfolio is likely to suffer during all but truly exceptional periods. More precisely, the VaR is the maximum loss that an institution can be confident it would lose a certain fraction of the time over a particular period. The power of the concept is its generality. VaR measures are applicable to entire portfolios - encompassing many asset categories and multiple sources of risk. As with its power, the challenge of calculating VaR also stems from its generality. In order to measure risk in a portfolio using VaR, some means must be found for determining a return distribution for the portfolio. There exists a wide range of literature on different methods of implementing VaR. But, when one attempts to apply the results, several questions remain open. For example, given a VaR measure, how can the risk manager test that the particular measure at hand is appropriately specified? And secondly, given two different VaR measures, how can the risk manager pick the best measure? Despite the popularity of VaR for measuring market risk, no consensus has yet been reach as to the best method to implement this risk measure. The absence of consensus is in part derived from the realization that each method currently in use has some significant drawbacks. The aim of this project is threefold: to introduce the reader to the concept of VaR; present the theoretical basis for the general approaches to VaR computations; and to introduce and apply Extreme Value Theory to VaR calculations. The general approaches to VaR computation falls into three categories, namely, Analytic (Parametric) Approach, Historical Simulation Approach, and Monte Carlo Simulation Approach. Each of these approaches has its strengths and weaknesses, which will study more closely. The extreme value approach to VaR calculation is a relatively new approach. Since most observed returns are central ones, traditional VaR methods tend to ignore extreme events and focus on risk measures that accommodate the whole empirical distribution of central returns. The danger of this approach is that these models are prone to fail just when they are needed most - in large market moves, when institutions can suffer very large losses. The extreme value approach is a tool that attempts to provide the user with the best possible estimate of the tail area of the distribution. Even in the absence of useful historical data, extreme value theory provides guidance on the kind of distribution that should be selected so that extreme risks are handled conservatively. As an illustration, the extreme value method will be applied to a foreign exchange futures contract. The validity of EVT to VaR calculations will be tested by examining the data of the Rand/Dollar One Year Futures Contracts. An extended worked example will be provided wherein which attempts to highlight the considerable strengths of the methods as well as the pitfalls and limitations. These results will be compared to VaR measures calculated using a GARCH(l,l) model.
AFRIKAANSE OPSOMMING: Handelsbanke, aksepbanke, assuransiemaatskappye, nie-finansiële instellings en pensioenfondse beskik oor portefeuljes van finansiële bates soos aandele, effekte, geldeenhede en afgeleides. Elke instelling moet die omvang kan bepaal van die risiko waaraan die portefeulje blootgestel is in die loop van 'n dag, week, maand of jaar. Uitsonderlike gebeure op finansiële markte, soos die ineenstorting van die aandelemark in Oktober 1987, is van besondere belang vir finansies en veral vir risikobestuur en finansiële regulering. 'n Metode wat genoem word Waarde op Risiko (WoR), kan gebruik word om markverliese te meet. WoR is 'n kragtige maatstaf vir risiko en word deur vele instellings gebruik vir die bestuur van mark-risiko. Waarde op Risiko is 'n raming van die grootste verlies wat 'n portefeulje moontlik kan ly gedurende enige tydperk, met uitsluiting van werklik uitsonderlike tydperke. Van nader beskou, is WoR die maksimum verlies wat 'n instelling kan verwag om gedurende 'n sekere tydperk binne 'n bepaalde periode te ly. Die waarde van die konsep lê in die algemene aard daarvan. WoR metings is van toepassing op portefeuljes in dié geheel en dit omvat baie kategorieë bates en veelvuldige bronne van risiko. Soos met die waarde van die konsep, hou die uitdaging om WoR te bereken ook verband met die algemene aard van die konsep. Ten einde die risiko te bepaal in 'n portefeulje waar WoR gebruik word, moet metodes gevind word waarvolgens 'n opbrengsverdeling vir die portefeulje vasgestel kan word. Daar bestaan 'n groot verskeidenheid literatuur oor die verskillende metodes om WoR te implementeer. Wanneer dit egter kom by die toepassing van die resultate, bly verskeie vrae onbeantwoord. Byvoorbeeld, hoe kan die risikobestuurder aan die hand van 'n gegewe WoR-maatstaf toets of die spesifieke maatstaf reg gespesifiseer is? Tweedens, hoe kan die risikobestuurder die beste maatstaf kies in die geval van twee verskillende WoR-maatstawwe? Ondanks die feit dat WoR algemeen gebruik word vir die meting van markrisiko, is daar nog nie konsensus bereik oor die beste metode om hierdie benadering tot risikometing te implementeer nie. Die feit dat daar nie konsensus bestaan nie, kan deels daaraan toegeskryf word dat elkeen van die metodes wat tans gebruik word, ernstige leemtes het. Die doel van hierdie projek is om die konsep WoR bekend te stel, om die teoretiese grondslag te lê vir die algemene benadering tot die berekening van WoR en om die Ekstreme Waarde-teorie bekend te stel en toe te pas op WoR-berekenings. Die algemene benadering tot die berekening van WoR word in drie kategorieë verdeel naamlik die Analitiese (Parametriese) benadering, die Historiese simulasiebenadering en die Monte Carlo-simulasiebenadering. Elkeen van die benaderings het sterk- en swakpunte wat van nader ondersoek sal word. Die Ekstreme Waarde-benadering tot WoR is 'n relatief nuwe benadering. Aangesien die meeste opbrengste middelwaarde-gesentreer is, is tradisionele WoR-metodes geneig om uitsonderlike gebeure buite rekening te laat en te fokus op risiko-maatstawwe wat die hele empiriese verdeling van middelwaarde-gesentreerde opbrengste akkommodeer. Die gevaar bestaan dan dat hierdie modelle geneig is om te faal juis wanneer dit die meeste benodig word, byvoorbeeld in die geval van groot markverskuiwings waartydens organisasies baie groot verliese kan ly. Daar word beoog om met behulp van die Ekstreme Waarde-benadering aan die gebruiker die beste moontlike skatting van die stert-area van die verdeling te gee. Selfs in die afwesigheid van bruikbare historiese data verskaf die Ekstreme Waarde-teorie riglyne ten opsigte van die aard van die verdeling wat gekies moet word, sodat uiterste risiko's versigtig hanteer kan word. Ten einde hierdie metode te illustreer, word dit in hierdie studie toegepas op 'n termynkontrak ten opsigte van buitelandse wisselkoerse. Die geldigheid van die Ekstreme Waarde-teorie ten opsigte van WoR berekenings word getoets deur die data van die Rand/Dollar Eenjaartermynkontrak te bestudeer. 'n Volledig uitgewerkte voorbeeld word verskaf waarin die slaggate en beperkings asook die talle sterkpunte van die model uitgewys word. Hierdie resultate sal vergelyk word met 'n WoR-meting wat bereken is met die GARCH (1,1) model.

As federal fire management policies shifted from complete fire suppression to recognizing wildfire as essential to forest ecosystems, the responsibility for managing wildfire risk has shifted from the federal government to being shared with communities and individuals, particularly in the wildland-urban interface (WUI) where large populations live adjacent to fire prone environments. Understanding the relationship between knowledge, perception, and behavior is critical in these areas because the actions, or inactions, of a few individuals can create hazardous conditions that affect the entire community.

This thesis utilizes qualitative methods to explore the perceptions of permanent residents in the Big Bear Valley regarding fire risk, mitigation, and community outreach and education efforts. Results indicate that residents are knowledgeable about fire risk, obtain information from varying sources, and do take action to mitigate risks on their properties.

Value-at-Risk (VaR) models provide quantile forecasts for future returns. If a loss is greater than or equal to the corresponding VaR forecast, we have a breach. A VaR model is usually validated by considering realized breach sequences. Several statistical tests exist for this purpose, called backtests. This paper presents an extensive study of the statistical power for the most recognized backtests. We simulate returns and estimate VaR forecasts, resulting in breach sequences not satisfying the null hypothesis of the backtests. We apply the backtests on the data, and assess their ability to reject misspecified models. The Geometric conditional coverage test by Berkowitz et al. (2011) performs best. A minimum amount of observations is needed to make inference with satisfying power. A sample size of 250 data points, which is the minimum requirement set by the Basel Committe on Banking Supervision (2011), is not sufficient. The common implementation of the Dynamic Quantile test, by Engle and Manganelli (2004), has a too high rejection rate for correctly specified VaR models.

Defense date: 15/01/2010
Examining Board: Professor Pascal Courty, University of Victoria, Canada, Supervisor Professor Fernando Vega-Redondo, EUI Professor Roberto Serrano, Brown University Professor Robert Sugden, University of East Anglia
The topic of this thesis is decision-making under risk. I focus my analysis on expected utility theory by von Neumann and Morgenstern. I am especially interested in modeling risk attitudes represented by Bernoulli utility functions that belong to the following classes: Constant Absolute Risk Aversion, Decreasing Absolute Risk Aversion (understood as strictly decreasing) and in particular a subset thereof - Constant Relative Risk Aversion. I build a theory of buying and selling price for a lottery, the concepts defined by Raiffa, since such theory proves useful in analyzing a number of interesting issues pertaining to risk attitudes' characteristics within expected utility model. In particular, I analyze the following: - Chapter 2 - expected utility without consequentialism, buying/selling price gap, preference reversal, Rabin paradox - Chapter 3 - characterization results for CARA, DARA, CRRA, simple strategies and an extension of Pratt result on comparative risk aversion - Chapter 4 - riskiness measure and its intuition, extended riskiness measure and its existence, uniqueness and properties

博士
淡江大學
財務金融學系博士班
95
This study focuses on VaR measurement and VaR-based hedge ratio, and it contains three parts. The first part is titled “Estimation of Value-at-Risk under Jump Dynamics and Asymmetric Information”, the second part is named “Hedging with Zero-Value at Risk Hedge Ratio”, and the last one is “Bivariate Markov Regime Switching Model for Estimating Multi-period zero-VaR Hedge Ratios and Minimum Variance Hedge Ratios”. A brief introduction of these three parts is described as follow: The first part employs GARJI, ARJI and asymmetric GARCH models to estimate the one-step-ahead relative VaR and compare their performances among these three models. Two stock indices (Dow Jones industry index and S&P 500 index) and one exchange rate (Japanese yen) are used to estimate the model-based VaR, and we investigate the influences of price jumps and asymmetric information on the performance of VaR measurement. The empirical results demonstrate that, while asset returns exhibited time-varying jump and the information asymmetric effect, the GARJI-based and ARJI-based VaR provide reliable accuracy at both low and high confidence levels. Moreover, as MRSB indicates, the GARJI model is more efficient than alternatives. In the second part, a mean-risk hedge ratio is derived on the foundation of Value-at-Risk. The proposed zero-VaR hedge ratio converges to the MV hedge ratio under a pure martingale process or an infinite risk-averse level. In empirical section, a bivariate constant correlation GARCH(1,1) model with an error correction term is adopted to calculate zero-VaR hedge ratio, and we compare it with the one proposed by Hsin et al. (1994) which maximized the utility function as their objective. The last part extends one period zero-VaR hedge ratio (Hung et al., 2006) to the multi-period case, and also employed a four-regime bivariate Markov regime switching model and diagonal VECH GARCH(1,1) model to estimate both zero-VaR and MV hedge ratios for Dow Jones and S&P 500 stock indices. Dissimilar with Bollen et al. (2000), the in-sample fitting abilities and out-of-sample variance forecasts between regime-switching and GARCH approaches are investigated in a bivariate case through in- and out-of-sample hedging performances. The empirical evidences show that the regime switching approach provides better in-sample fitting ability; however, GARCH approach has better out-of-sample variance forecast ability for most cases.

碩士
中原大學
國際貿易研究所
97
Abstract As the financial derivatives been rapidly developed, various kinds of investment tools have been constantly renovateing. In fact, Markowitz’s portfolio concept is still the benchmark for most investment behavior in the financial market. Although the innovation of investment tools and related financial derivatives can offer more scattered fund for financial market, more risk derived from the fluctuation of asset price comes with that. Therefore, the concept of risk management becomes more important for investors and managers. Based on this reason, this study combines the concept of VaR with the theory of portfolio to investigate how should investors analyze and manage the VaR under the chosen optimum portfolio. The 10 component assets in portfolio contain foreign exchange rates, stocks, mutual funds and gold. By using Mean-Variance approach and individual investor’s risk aversion altitude, we can first decide optimal investment portfolio, including component assets and their weights. Furthermore, employing historical simulation, Mote Carlo simulation combined with GARCH model, and EGARCH model we can evaluate the VaR of that optimal portfolio. Finally, through the RMSE, MAE and back test we can evaluate each model’s forecasting performance. Empirical study shows that during the period of Subprime Mortgage storm (the stage of economic recession), investors should invest in gold market to get better hedge and preserve asset value, and the decided optimal portfolio can actually reduce investment risk. Moreover, from the results of the out-of-sample forecasting we know that the metempirical model to GARCH of Monte Carlo Simulation is the best one to forecast the VaR, and the Historical Simulation and EGARCH model have over-evaluated the VaR.

碩士
國立臺灣大學
財務金融學研究所
89
Market risk management traditionally focused on the distribution of portfolio value changes resulting from moves in each asset price. Hence the market risk is really a pure form；risk in an idealized market with no friction in obtaining the fair price. However, many markets had an additional liquidity component that arises from a trader did not realized the price we see when liquidating his position. We argue that the deviation of the liquidation price from the market price we see should be added into our risk measures in order to capture the true level of overall market risk. With no previous paper mentioned, we put our view on liquidity risk resulting from price limit. Although the asset price has been fixed, there are no traders on the other side. We argue that liquidity risk associated with price limit, particularly for portfolios composed of high turnover or high volatility securities, is an important part of overall risk and is therefore an important component to model. We develop a simple liquidity risk method, holding-risk-return measure, that can be easily incorporated into standard value-at-risk models. We show that ignoring the liquidity effect arising from price limit can produce underestimates of market risk by as much as 26%-30%. Furthermore, we firmly recommend that FIs and supervisors who use value-at-risk as market risk management tool should start monitoring liquidity risk due to price limit, particularly if their portfolios are concentrated in high turnover securities. Also, managers should be aware of other important risk factors that are not properly handled in value-at-risk model.

碩士
東吳大學
商用數學系
90
Value at Risk (VaR) has become the standard tool used by many financial institutions to measure market risk. However, a VaR estimator may be affected by sample variation or estimation risk. Accordingly, the concept of risk in Value at Risk introduced by Jorion (1996) should be concerned. That is, we should cautiously look at the VaR and better use it with its confidence interval. After surveying several existing procedures proposed by Jorion (1996), Huschens (1997), and Ridder (1997), we propose a new way to measure the risk in Value at Risk in this paper. We compare their performances through Monte Carlo simulations and empirical works and find that the new method provides better accuracy and robustness in the estimation of the risk in VaR.

碩士
國立交通大學
土木工程學系
100
There are many risk factors at each stage in project’s life cycle, each execution factors are likely to give many risks results and increase the uncertainty of this project,also the job achieve time or total finalization may have the negative effect, the effects can cause the huge odds for actual completion. Consider all risks must use to cover the whole environmental factors and with the construction time to update the risk prediction tool that may occur in the case. The study of this project, using the earned value management methods for performance evaluation - Value At Risk, VAR, forecast the project completion schedule by adding value at risk concept of the probability level, the project may confront risks to this forecast in real reaction completed on schedule, to help project managers to more effective management. After ascertaining the model, the schedule at risk used in practice to respond the results of the analysis in the case, and the different between the schedule at risk and the Earned Value Management forecast completion schedule, besides, schedule at risk and the actual completion of the remaining duration to compare the differences discussed.

碩士
南華大學
財務金融學系財務管理碩士班
102
Using hand-collected data on top 500 banks around the world, this theses empirically investigates the joint impacts of risk disclosure and internal risk management on bank Value-at-Risk (VaR) in context of international evidence. Our empirical evidences indicate that banks with higher quality of risk disclosure and better risk management show lower VaR. Regarding the bank corporate governance, banks with higher board compensations and independent board ratio would significantly reduce bank’s downside risk while banks with larger boards would increase bank VaR. Banks with higher degree of income diversification enjoy lower downside risk, especially in higher capital ratio of banking sector.

碩士
國立臺灣大學
財務金融學研究所
97
Extreme returns are of the most concern to investors and regulators. Risk management is the key to reduce the impact of extreme returns. Value at Risk (VaR) has been used as a measure of risk. VaR estimates the largest potential loss to investors in a specified investment horizon at the specified confidence interval. Various VaR models have been developed under different assumptions. The extreme value theory (EVT) fits only the extreme values to a distribution instead of taking the whole distribution into consideration. We seek to apply the EVT to calculate the VaR and compare it to other models in this paper. We use five VaR models (SMA, EWMA, historical simulation, EVT estimated by MLE and PWM) and calculate VaR for two time horizons, one excludes the financial tsunami and the other one includes it. The measure of accuracy and the measure of conservatism are conducted for evaluation. The evaluation results indicate that with the utilization of the EVT, the VaR is more accurate and conservative than other traditional methodologies. We also apply the EVT to calculate the equity risk of C-1 risk factor in the risk-based capital (RBC) formula. The equity risk is measured by both the original RBC formula and the EVT. The results tell us that the equity risk estimated by the EVT is higher, which means that it is more conservative than the original formula. Since we take only extreme returns within each block into calculation, chances are that the ignorance of other values might unreliable results. More discussion of the EVT application to insurance can be conducted in the future. We provide a new point of view for the insurance regulators while setting regulations for insurance companies.

Futures contracts represent a suitable instrument for hedging. One conse- quence of their standardized nature is the presence of basis risk. In order to mitigate it an agent might aim to minimize Value at Risk or Expected Shortfall. Among numerous approaches to their modelling, CAViaR models which build upon quantile regression are appealing due to the limited set of assumptions and decent empirical performance. We propose alternative specifications for CAViaR model - power and exponential CAViaR, and an alternative, flexible way of computing Expected Shortfall within CAViaR framework - Implied Expectile Level. Empirical analysis suggests that ex- ponential CAViaR yields competitive results both in Value at Risk and Ex- pected Shortfall modelling and in subsequent Value at Risk and Expected Shortfall hedging. 1

碩士
國立交通大學
土木工程學系
100
Generally, project risk management focuses on the ex ante works - risk identification, risk analysis and risk response, expecting to reduce the possibility of facing severe problems caused by risk factors. However, there are still a lot of risk factors that are unexpectable. In order to set up a complete risk management strategy, it is important to know how to quantify the risk. In project management technology, Earned Value Management System (EVMS) is considered one of the best methods in many countries. Recently, research and application in EVMS has become more and more popular. As EVMS being well developed, it would be more complete and more applicable for project management if there is a mechanism that monitors project risk and performance regularly, and reports the quantified value. Therefore, this study will establish a regular monitoring mechanism – Budget at Risk Model. The concept of project cost risk quantification comes from Value at Risk, using statistical distributions, confidence level and critical value.

碩士
東吳大學
經濟學系
89
Abstract The level of market risk is expressed by variety in most financial theories. However what variety can be is only the entire scatter degree of financial variables. As for market risk , what scary most is not the fluctuation of daily financail variables but the influence which is not often caused in probabilty distribution while the financial market collapses. Market risk is not enough simlpy to be explained by variety. Therefore , in order to estimate market risk , it is necessary to present a risk-measured index which shows the most probable potential loss in the market. In 1994 , J.P. Morgan Company developed a Value at Risk Model where left-tailed probabilty distribution is emphasized through the conceot of probability distribution in statistics. This model is used to count the most possible amount which the company may lose in next twenty four hours in its global investment. Since the model emphasizes the loss , it is easy to understand and it also gets rid of the disadvange caused by using variety on risk control. Hence, VaR model is discussed and used a lot pratically and academically. With the birth of derivatives , the financial market becomes more plural. But due to the high leverage of derivatives , the loss resuled from unproper investment is even considerable. So financial authorities in each country all put a high premium in risk control of derivatives. Nevertheless derivatives are far different from genaral linear-rewarded financial products owint to their non-linear rewarded character. In this complicated financial market , traditional risk valus models can''t estimate market risk exactly so that risk controllers may know how to avoid it properly. Thus the major theme in this study is to find out a method which can assess the risk value of derivatives more precisely. However due to minor sorts if derivatives in Taiwan and limited information , We make option in real experiment here. At the same time , we use traditional first order Delta and Second order Delta-Gamma , because option is highly related with vioality financial tool , so we use historical vioality , Garch model , and implied vioality to catch this feature . Besides , we also use extreme value to compare with traditional VaR model .

碩士
國立暨南國際大學
國際企業學系
91
Value-at-Risk (VaR) models have been radically developed to measure the market risk. In this paper, we apply both hypothesis-testing and relative performance criteria to evaluate different VaR models. The results suggest that both SWARCH-L model and adjusted-historical simulation model have better performance across all criteria. The strength of SWARCH approach is its efficiency to track the evolution of risk in terms of its highest correlation, only it tends to produce too few exceptions. For future researches, we suggest it may be more accurate to allow for more than two regimes or to add the GARCH term in practice.