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In the recent literature, methods from extreme value theory (EVT) have frequently been applied for the estimation of tail risk measures. While previous analyses show that EVT methods often lead to accurate estimates for risk measures, a potential drawback lies in high standard errors of point estimates of these methods as only a fraction of the data set is used. Thus, the aim of this paper is to comprehensively study the impact of model risk on EVT methods when determining the Value-at-Risk and Expected Shortfall. We distinguish between misspecification, estimation and prediction risk and show that methods from extreme value theory are less prone to misspecification and estimation risk, however, they exhibit a higher sensitivity towards prediction risk. We find that this can lead to more severe Value-at-Risk and Expected Shortfall underestimations than for traditional estimation methods in extreme cases. Hence, we show how sources of model risk should be taken into account for the quantification of capital requirements, in order to provide sufficient capital levels in the presence of model risk.
Extreme Value Modeling and Risk Analysis: Methods and Applications presents a broad overview of statistical modeling of extreme events along with the most recent methodologies and various applications. The book brings together background material and advanced topics, eliminating the need to sort through the massive amount of literature on the subje
Extreme value theory (EVT) deals with extreme (rare) events, which are sometimes reported as outliers. Certain textbooks encourage readers to remove outliers—in other words, to correct reality if it does not fit the model. Recognizing that any model is only an approximation of reality, statisticians are eager to extract information about unknown distribution making as few assumptions as possible. Extreme Value Methods with Applications to Finance concentrates on modern topics in EVT, such as processes of exceedances, compound Poisson approximation, Poisson cluster approximation, and nonparametric estimation methods. These topics have not been fully focused on in other books on extremes. In addition, the book covers: Extremes in samples of random size Methods of estimating extreme quantiles and tail probabilities Self-normalized sums of random variables Measures of market risk Along with examples from finance and insurance to illustrate the methods, Extreme Value Methods with Applications to Finance includes over 200 exercises, making it useful as a reference book, self-study tool, or comprehensive course text. A systematic background to a rapidly growing branch of modern Probability and Statistics: extreme value theory for stationary sequences of random variables.
In this paper the authors introduce a new hybrid approach based on the Extreme Value Theory (EVT) to joint estimation of Value at Risk (VaR) and Expected Shortfall (ES) for high quantiles of return distributions. The approach is suitable for measuring market risk in the emerging markets. It is designed to capture the empirical features of returns with emerging markets, such as leptokurtosis, asymmetry, autocorrelation and heteroscedasticity.
Directly oriented towards real practical application, this book develops both the basic theoretical framework of extreme value models and the statistical inferential techniques for using these models in practice. Intended for statisticians and non-statisticians alike, the theoretical treatment is elementary, with heuristics often replacing detailed mathematical proof. Most aspects of extreme modeling techniques are covered, including historical techniques (still widely used) and contemporary techniques based on point process models. A wide range of worked examples, using genuine datasets, illustrate the various modeling procedures and a concluding chapter provides a brief introduction to a number of more advanced topics, including Bayesian inference and spatial extremes. All the computations are carried out using S-PLUS, and the corresponding datasets and functions are available via the Internet for readers to recreate examples for themselves. An essential reference for students and researchers in statistics and disciplines such as engineering, finance and environmental science, this book will also appeal to practitioners looking for practical help in solving real problems. Stuart Coles is Reader in Statistics at the University of Bristol, UK, having previously lectured at the universities of Nottingham and Lancaster. In 1992 he was the first recipient of the Royal Statistical Society's research prize. He has published widely in the statistical literature, principally in the area of extreme value modeling.
In this book Simona Roccioletti reviews several valuable studies about risk measures and their properties; in particular she studies the new (and heavily discussed) property of "Elicitability" of a risk measure. More important, she investigates the issue related to the backtesting of Expected Shortfall. The main contribution of the work is the application of "Test 1" and "Test 2" developed by Acerbi and Szekely (2014) on different models and for five global market indexes.
Financial Risk Forecasting is a complete introduction to practical quantitative risk management, with a focus on market risk. Derived from the authors teaching notes and years spent training practitioners in risk management techniques, it brings together the three key disciplines of finance, statistics and modeling (programming), to provide a thorough grounding in risk management techniques. Written by renowned risk expert Jon Danielsson, the book begins with an introduction to financial markets and market prices, volatility clusters, fat tails and nonlinear dependence. It then goes on to present volatility forecasting with both univatiate and multivatiate methods, discussing the various methods used by industry, with a special focus on the GARCH family of models. The evaluation of the quality of forecasts is discussed in detail. Next, the main concepts in risk and models to forecast risk are discussed, especially volatility, value-at-risk and expected shortfall. The focus is both on risk in basic assets such as stocks and foreign exchange, but also calculations of risk in bonds and options, with analytical methods such as delta-normal VaR and duration-normal VaR and Monte Carlo simulation. The book then moves on to the evaluation of risk models with methods like backtesting, followed by a discussion on stress testing. The book concludes by focussing on the forecasting of risk in very large and uncommon events with extreme value theory and considering the underlying assumptions behind almost every risk model in practical use – that risk is exogenous – and what happens when those assumptions are violated. Every method presented brings together theoretical discussion and derivation of key equations and a discussion of issues in practical implementation. Each method is implemented in both MATLAB and R, two of the most commonly used mathematical programming languages for risk forecasting with which the reader can implement the models illustrated in the book. The book includes four appendices. The first introduces basic concepts in statistics and financial time series referred to throughout the book. The second and third introduce R and MATLAB, providing a discussion of the basic implementation of the software packages. And the final looks at the concept of maximum likelihood, especially issues in implementation and testing. The book is accompanied by a website - www.financialriskforecasting.com – which features downloadable code as used in the book.
Value at Risk (VaR) and Expected Shortfall (ES) are methods often used to measure market risk. Inaccurate and unreliable Value at Risk and Expected Shortfall models can lead to underestimation of the market risk that a firm or financial institution is exposed to, and therefore may jeopardize the well-being or survival of the firm or financial institution during adverse markets. The objective of this study is therefore to examine various Value at Risk and Expected Shortfall models, including fatter tail models, in order to analyze the accuracy and reliability of these models. Thirteen VaR and ES models under three main approaches (Parametric, Non-Parametric and Semi-Parametric) are examined in this study. The results of this study show that the proposed model (ARMA(1,1)-GJR-GARCH(1,1)-SGED) gives the most balanced Value at Risk results. The semi-parametric model (Extreme Value Theory, EVT) is the most accurate Value at Risk model in this study for S&P 500.
Master's Thesis from the year 2007 in the subject Business economics - Banking, Stock Exchanges, Insurance, Accounting, grade: 1 (A), University of Graz (Institut für Finanzwirtschaft), language: English, abstract: This thesis provides an exhaustive and well-founded overview of risk measures, in particular of Value at Risk (VaR) and risk measures beyond VaR. Corporations are exposed to different kinds of risks and therefore risk management has become a central task for a successful company. VaR is nowadays widely adapted internationally to measure market risk and is the most frequently used risk measure amongst practitioners due to the fact that the concept offers several advantages. However, VaR also has its drawbacks and hence there have been and still are endeavours to improve VaR and to find better risk measures. In seeking alternative risk measures to try to overcome VaR's disadvantages, while still keeping its advantages, risk measures beyond VaR were introduced. The most important alternative risk measures such as Tail Conditional Expectation, Worst Conditional Expectation, Expected Shortfall, Conditional VaR, and Expected Tail Loss are presented in detail in the thesis. It has been found that the listed risk measures are very similar concepts of overcoming the deficiencies of VaR and that there is no clear distinction between them in the literature - 'confusion of tongues' would be an appropriate expression. Two concepts have become widespread in the literature in recent years: Conditional VaR and Expected Shortfall, however there are situations where it can be seen that these are simply different terms for the same measure. Additionally other concepts are touched upon (Conditional Drawdown at Risk, Expected Regret, Spectral Risk Measures, Distortion Risk Measures, and other risk measures) and modifications of VaR (Conditional Autoregressive VaR, Modified VaR, Stable modelling of VaR) are introduced. Recapitulatory the basic findings of the thesis are that t