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1
Tran, Manh. "Value-at-risk estimates." Thesis, Aston University, 2018. http://publications.aston.ac.uk/37813/.
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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.
2
Novák, Martin. "Value at Risk models for Energy Risk Management." Master's thesis, Vysoká škola ekonomická v Praze, 2010. http://www.nusl.cz/ntk/nusl-71889.
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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.
3
Heidrich, Matthias [Verfasser]. "Conditional Value-at-Risk Optimization for Credit Risk Using Asset Value Models / Matthias Heidrich." München : Verlag Dr. Hut, 2012. http://d-nb.info/1020299681/34.
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Hager, Peter. "Corporate Risk Management : Cash Flow at Risk und Value at Risk /." Frankfurt am Main : Bankakademie-Verl, 2004. http://www.gbv.de/dms/zbw/378196367.pdf.
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5
Samiei, Saeid. "Studies in value-at-risk." Thesis, Cardiff University, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.273586.
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6
CARVALHO, RENATO RANGEL LEAL DE. "EXTREME VALUE THEORY: VALUE AT RISK FOR FIXED-INCOME ASSETS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2006. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=8245@1.
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CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO<br>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.<br>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.
7
PIRES, GUSTAVO LOURENÇO GOMES. "EXTREME VALUE THEORY: VALUE AT RISK FOR VARIABLE-INCOME ASSETS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2008. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=11850@1.
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COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR<br>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.<br>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.
8
Sampid, Marius Galabe. "Refining Value-at-Risk estimates : an extreme value theory approach." Thesis, University of Essex, 2018. http://repository.essex.ac.uk/22776/.
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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.
9
Karlsson, Malin, and Jonna Flodman. "Value at Risk : A comparison of Value at Risk models during the 2007/2008 financial crisis." Thesis, Örebro universitet, Handelshögskolan vid Örebro universitet, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:oru:diva-16023.
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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.
10
Weisner, Torben. "Value-at-Risk and Extreme Events." Thesis, Uppsala University, Department of Mathematics, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-130471.
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<p>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.</p><p>Estimation of Value-at-Risk is done using the two different frame-works: Historical simulation (regular and the Hybrid approach) andparametric (conditional heteroscedastic) models.</p><p>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.</p><p>Quantile regression as by Koenker (1978) is used for the parameterestimation of the Historical simulation models used.</p><p>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).</p><p>It is found that the present approach to Value-at-Risk estimationcan not be considered redundant due to the extreme events of theFinancial Crisis.</p>
11
Powell, Robert. "Industry value at risk in Australia." Thesis, Edith Cowan University, Research Online, Perth, Western Australia, 2007. https://ro.ecu.edu.au/theses/297.
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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.
12
Cecchinato, Nedda. "Forecasting time-varying value-at-risk." Thesis, Queensland University of Technology, 2010. https://eprints.qut.edu.au/32185/1/Nedda_Cecchinato_Thesis.pdf.
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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.
13
Broll, Udo, Andreas Förster, and Wilfried Siebe. "Market Risk: Exponential Weightinh in the Value-at-Risk Calculation." Technische Universität Dresden, 2020. https://tud.qucosa.de/id/qucosa%3A72009.
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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.
14
Norberg, Markus, and Johanna Petersson. "Artificial Value-at-Risk : Using Neural Networks to Replicate Filtered Historical Simulation for Value-at-Risk Calculations." Thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-185054.
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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.
15
Tolikas, Konstantinos. "An application of extreme value theory in value-at-risk estimation." Thesis, University of Dundee, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.491268.
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Ganief, Moegamad Shahiem. "Development of value at risk measures : towards an extreme value approach." Thesis, Stellenbosch : Stellenbosch University, 2001. http://hdl.handle.net/10019.1/52189.
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Thesis (MBA)--Stellenbosch University, 2001.<br>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.<br>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.
17
Ngwenza, Dumisani. "Quantifying Model Risk in Option Pricing and Value-at-Risk Models." Master's thesis, Faculty of Commerce, 2019. http://hdl.handle.net/11427/31059.
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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.
18
Ansaripoor, Amir Hossein. "Risk management in sustainable fleet replacement using conditional value at risk." Thesis, Cergy-Pontoise, Ecole supérieure des sciences économiques et commerciales, 2014. http://www.theses.fr/2014ESEC0006.
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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<br>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
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Malfas, Gregory P. "Historical risk assessment of a balanced portfolio using Value-at-Risk." Link to electronic thesis, 2004. http://www.wpi.edu/Pubs/ETD/Available/etd-0430104-025952/.
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Quintanilla, Maria T. "An asymptotic expansion for value-at-risk." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp01/MQ29264.pdf.
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Cheuk, Wai Lun. "Value at risk and the distortion operator." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/MQ59273.pdf.
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Røynstrand, Torgeir, Nils Petter Nordbø, and Vidar Kristoffer Strat. "Evaluating power of Value-at-Risk backtests." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for industriell økonomi og teknologiledelse, 2012. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-20961.
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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.
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Jimaale, Abdi. "Value at Risk : Utvärdering av fyra volatilitetsmodeller." Thesis, Örebro universitet, Handelshögskolan vid Örebro Universitet, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:oru:diva-37805.
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Kyriacou, Marios Nicou. "Financial risk measurement and extreme value theory." Thesis, University of Cambridge, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.621397.
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Yang, Shuai. "Jumps, realized volatility and value-at-risk." Thesis, University of Exeter, 2012. http://hdl.handle.net/10036/3893.
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This thesis consists of three research topics, which together study the related topics of volatility jumps, modeling volatility and forecasting Value-at-Risk (VaR). The first topic focuses on volatility jumps based on two recently developed jumps detection methods and empirically studied six markets and the distributional features, size and intensity of jumps and cojumps. The results indicate that foreign exchange markets have higher jump intensities, while equity markets have a larger jump size. I find that index and stock markets have more interdependent cojumps across markets. I also find two recently proposed jump detection methods deliver contradictory results of jump and cojump properties. The jump detection technique based on realized outlyingness weighted variation (ROWV) delivers higher jump intensities in foreign exchange markets, whereas the bi-power variation (BV) method produces higher jump intensities in equity markets. Moreover, jumps under the ROWV method display more serial correlations than the BV method. The ROWV method detects more cojumps and higher cojumps intensities than the BV method does, particularly in foreign exchange markets. In the second topic, the Model Confidence Set test (MCS) is used. MCS selects superior models by power in forecasting ability. The candidate models set included 9 GARCH type models and 8 realized volatility models. The dataset is based on six markets spanning more than 10 years, avoiding the so-called data snooping problem. The dataset is extended by including recent financial crisis periods. The advantage of the MCS test is that it can compare models in a group, not only in a pair. Two loss functions that are robust to noise in volatility proxy were also implemented and the empirical results indicated that the traditional GARCH models were outperformed by realized volatility models when using intraday data. The MCS test based on MSE selected asymmetric ARFIMA models and the HAR mode as the most predictive, while the asymmetric QLike loss function revealed the leveraged HAR and leveraged HAR-CJ model based on bi-power variation as the highest performers. Moreover, results from the subsamples indicate that the asymmetric ARFIMA model performs best over turbulent periods. The third topic focuses on evaluating a broad band of VaR forecasts. Different VaR models were compared across six markets, five volatility models, four distributions and 8 quantiles, resulting in 960 specifications. The MCS test based on regulatory favored asymmetric loss function was applied and the empirical results indicate that the proposed asymmetric ARFIMA and leveraged HAR models, coupled with generalized extreme value distribution (GEV) or generalized Pareto distribution (GPD), have the superior predictive ability on both long and short positions. The filtered extreme value methods were found to handle not only extreme quantiles but also regular ones. The analysis conducted in this thesis is intended to aid risk management, and subsequently reduce the probability of financial distress in the sector.
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Ferretti, Nicola <1998>. "Extreme Value Theory for Portfolio Risk Management." Master's Degree Thesis, Università Ca' Foscari Venezia, 2022. http://hdl.handle.net/10579/21806.
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This paper provides an overview of the role of extreme value theory in risk management as a method for modelling and measuring extreme risks. In particular, it is shown the peaks-over-threshold (POT) model and how this method provides a tool for estimating measures of tail risk like Value-at-Risk (VaR) and expected shortfall. Further topics of interest, including State-Space model, Block Maxima, Markowitz model and a real data application, are also discussed.
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Grönberg, Jonathan. "Study and Case of Wrong-Way Risk : Explorative Search for Wrong-Way Risk." Thesis, Karlstads universitet, Handelshögskolan (from 2013), 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-72689.
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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.<br>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.
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Seymour, Anthony. "Application of extreme value theory to the calculation of value-at-risk." Master's thesis, University of Cape Town, 2001. http://hdl.handle.net/11427/4930.
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Includes bibliographical references.<br>The main aim of the study was to test the applicability of published EVT-based VaR calculation methods to the South African market. Two methods were tested on a hypothetical portolio of South African stocks, using the standard backtesting technique.
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Siu, Kin-bong Bonny. "Expected shortfall and value-at-risk under a model with market risk and credit risk." Click to view the E-thesis via HKUTO, 2006. http://sunzi.lib.hku.hk/hkuto/record/B37727473.
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Siu, Kin-bong Bonny, and 蕭健邦. "Expected shortfall and value-at-risk under a model with market risk and credit risk." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2006. http://hub.hku.hk/bib/B37727473.
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Christodoulou, Michalis. "Covariance matrix estimation applied in value-at-risk and margin risk methodologies." Thesis, Imperial College London, 2005. http://hdl.handle.net/10044/1/8198.
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Eriksson, Kristofer. "Risk Measures and Dependence Modeling in Financial Risk Management." Thesis, Umeå universitet, Institutionen för fysik, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-85185.
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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.
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Coster, Rodrigo. "Comparando métodos de estimação de risco de um portfólio via Expected Shortfall e Value at Risk." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2013. http://hdl.handle.net/10183/76203.
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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.<br>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.
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Jui-Cheng, Hung. "Value-at-Risk Measures and Value-at-Risk based Hedging Approach." 2007. http://www.cetd.com.tw/ec/thesisdetail.aspx?etdun=U0002-1101200712485400.
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Hung, Jui-Cheng, and 洪瑞成. "Value-at-Risk Measures and Value-at-Risk based Hedging Approach." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/15961485385121826218.
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博士<br>淡江大學<br>財務金融學系博士班<br>95<br>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.
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鄭筱卉. "The Application of Value at Risk in Earned Value Management ─ Schedule At Risk." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/49295434092208013587.
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碩士<br>國立交通大學<br>土木工程學系<br>100<br>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.
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Tsai, Rou-Shin, and 蔡柔忻. "Risk Attitude、Optimal Portfolio and Value at Risk." Thesis, 2009. http://ndltd.ncl.edu.tw/handle/24533263559994455446.
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碩士<br>中原大學<br>國際貿易研究所<br>97<br>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.
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Chen, Shia-Ping, and 陳嘉平. "Liquidity Risk, Price Limit and Value at Risk." Thesis, 2001. http://ndltd.ncl.edu.tw/handle/03619778003822827691.
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碩士<br>國立臺灣大學<br>財務金融學研究所<br>89<br>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.
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Wu, Yi-Fang, and 吳一芳. "Estimation of the Risk in Value at Risk." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/19544859390224179649.
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碩士<br>東吳大學<br>商用數學系<br>90<br>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.
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LEWANDOWSKI, Michal. "Risk Attitudes and Measures of Value for Risky Lotteries." Doctoral thesis, 2010. http://hdl.handle.net/1814/13217.
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Defense date: 15/01/2010<br>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<br>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
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Hu, Shun-Ting, and 胡舜婷. "Application of Extreme Value Theory to Measure Value at Risk and Risk-Based Capital." Thesis, 2009. http://ndltd.ncl.edu.tw/handle/75641784529902308353.
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碩士<br>國立臺灣大學<br>財務金融學研究所<br>97<br>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.
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Svatoň, Michal. "Zajištění Value at Risk a podmíněného Value at Risk portfolia pomocí kvantilových autoregresivních metod." Master's thesis, 2015. http://www.nusl.cz/ntk/nusl-294263.
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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
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邱靜妤. "The Application of Value at Risk in Earned Value Management – Budget at Risk Model." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/59550824646407993892.
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碩士<br>國立交通大學<br>土木工程學系<br>100<br>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.
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Lee, Tung-Chin, and 李東錦. "Risk Disclosure,Risk Management,and Bank Value-at-Risk: International Study." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/05694821065905708100.
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碩士<br>南華大學<br>財務金融學系財務管理碩士班<br>102<br>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.
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Liu, Chih-Yung, and 劉志勇. "Value at Risk of Option." Thesis, 2001. http://ndltd.ncl.edu.tw/handle/29682964842112454979.
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碩士<br>東吳大學<br>經濟學系<br>89<br>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 .
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Tang, Wei-Ting, and 湯偉廷. "Evaluation of Value-at-Risk." Thesis, 2003. http://ndltd.ncl.edu.tw/handle/42661678645909130064.
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碩士<br>國立暨南國際大學<br>國際企業學系<br>91<br>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.
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Rodrigues, Pedro Diogo Guimarães. "Backtesting Value-at-Risk Models." Master's thesis, 2017. http://hdl.handle.net/1822/46454.
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Dissertação de mestrado em Finanças<br>In the last decades, Value-at-Risk has become one of the most popular risk measurements
techniques in the financial world. However, VaR models are only useful if they predict risk
accurately. In order to evaluate the quality of the VaR estimates, it is necessary to perform
appropriate and diverse backtesting methodologies.
In this study I test VaR estimates obtained from an unconditional parametric models (student-t
generalized error, skewed student-t, pareto, and Weibull distributions) for four stock market
indexes (DJIA, SP-500, Nikkei 225 and Dax 30) considering several different confidence levels.
A rolling function procedure is applied to estimate the models parameters through maximum
likelihood.
The performance of the VaR models is measured by applying several different tests of
Unconditional Coverage, Independence and Conditional Coverage.
The results of the backtests provide some indication of the possible problems of the models,
being the main one the independence property, leading us to conclude that they do not react
well under high turbulent times, and consequently exceptions are auto correlated and come in
clusters.<br>Durante as ultimas décadas, Value-at-Risk tornou-se uma das medidas de risco mais populares na
industria financeira. Todavia, os modelos VaR só são úteis se conseguirem fazer uma previsão
acertada do risco. De forma a avaliar a qualidade e precisão das estimativas de um modelo VaR,
é necessário utilizar uma metodologia apropriada de avaliação.
A principal contribuição desta dissertação consiste em estudos empíricos, onde diversos modelos
VaR paramétricos não condicionais são estimados para os quarto índices selecionados assumindo,
para cada um, utilizando um leque de cinco distribuições: Student t, Generalized Error, Skewed
Student t, Pareto e Weibull. Os parâmetros dos modelos são estimados por máxima verosimilhança
através de uma janela rolante.
A performance das estimativas VaR é medida aplicando testes de cobertura incondicional,
independência e cobertura condicional.
Os resultados da avaliação aos modelos mostrou alguns problemas, sendo o mais grave a falta de
independência entre as excepções, levando-nos a concluir que os modelos não reagem bem
durante períodos turbulentos, e consequentemente as excepções surge em grupos e estão
bastante correlacionadas.
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Chen, Shih-hui, and 陳世慧. "Value at Credit Risk-CreditMetrics." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/36112727071414386937.
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碩士<br>中國文化大學<br>會計研究所<br>90<br>This study applies the CreditMetrics model to evaluate credit risk by the factor of credit rating、recovery rate、probability of default and credit spread. The change of credit rating exists correlation between assets. That is why it needs to consider the correlation of credit rate change of the portfolio while evaluating the credit risk. But the existed methods could not provide the influence of group at some smaller region, like Taiwan.
The purpose of this study is to verify if the group correlation will influence the cor-relation of the credit rate change for Taiwan′s public companies. The method is to use the loan to the public listing companies as the portfolio of the 36 chosen banks in Tai-wan. Apply the CreditMetrics model and modify the transition matrix by economics situation. To find the effect of the group correlation and economics modification.
The study result indicates that : 1. Since the loss of the credit risk is not distributed averagely, the loss opportunity is higher than profit. And it is easy to be influenced by the system risk. Once the economics environment gets worse, the over situation will in-crease obviously. Through the economics modification, it could reflect the reality more. 2. While the economics environment is worse, the group correlation will effect more.
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施勇任. "Value-at-risk of option." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/49920182612404079200.
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碩士<br>東吳大學<br>商用數學系<br>90<br>In general, the delta method which employed first order Taylor’s expansion is used to approximate the relationship between derivatives and its underlying factors when the portfolio contain non-linear contract such as options. If the performance of delta method does not perform well enough, the second order Taylor’s expansion, called delta-gamma method, can be employed. There are two potential errors implied in the delta approximation and delta-gamma approximation. First, the error of distribution assumption will occur when the distribution of underlying is not a normal distribution. Second, the error will occur when option price calculated by delta approximation and delta-gamma approximation. In this paper we introduce the EGB2 distribution to describe the behavior of security return. The EGB2 distribution can directly characterize the leptokurtosis, fat tails and skewness of security return. Under the no arbitrage assumption, we employ the method of moment to estimate the parameters of EGB2 distribution through real market daily return. We also employ the GB2 option pricing formula, proposed by McDonald & Bookstaber (1991), to calculate the Value-at-Risk (VaR) of options for different methods.
In our empirical study, we select ten Taiwan warrant data during 1999 and 2001 and calculate their VaRs. Because the daily change rate of security return in Taiwan is limited within [-7%, 7%], the leptokurtosis of security return is not obvious. We find that the major factor affect the VaR of option is not option pricing model but the VaR of security when the security return is independently and identically distributed. Also, the analytical approach is better than delta method and delta-gamma method in the empirical results.
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Shih, Shin-hua, and 施欣華. "The Estimation of Value at Risk in the Exchange Rate - Comparing Value at Risk Models." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/2vwwxj.
Full textAbstract:
碩士<br>國立高雄應用科技大學<br>金融資訊研究所<br>95<br>The foreign exchange market is the biggest financial market in the world. The enterprise, having open foreign exchange position, always care the risk being caused by the fluctuation of exchange rate. The risk of exchange rate is caused by hedging incompletely. The careless and indiscreet in the risk of exchange rate possibly can bring about the global enterprise to have the significant loss and to reduce the competitive ability. Therefore it’s really important to construct the risk management system and to evaluate effectively the risk of exchange rate .
The purpose of my study is to use various Value at Risk models (Variance-Covariance Method, Historical Simulation Method, Monte Carlo Simulation Approach) for calculating VaR. Applying daily exchange rate data, this paper is to study five countries currencies such as Pound, Canadian Dollar, Japanese Yen, Euro Dollar and New Taiwan Dollar NTD against U.S. Dollars to compare the accuracy and efficiency of different Value at Risk models. According the empirical results, it shows the performance of Mote Carlo Simulation is better than Historical Simulation and Variance-Covariance Method. The VaR of MC Simulation is from 5000 replications. The times we take more trials, the MC Simulation model performs much well for accuracy measures.