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Author : Tomer Shushi
Publisher :
ISBN 13 :
Total Pages : 110 pages
Book Rating : 4.:/5 (993 download)
Download or read book Tail Risk Measures and Loss Distributions written by Tomer Shushi and published by . This book was released on 2016 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Katja Ignatieva
Publisher :
ISBN 13 :
Total Pages : 28 pages
Book Rating : 4.:/5 (13 download)
Download or read book Conditional Tail Risk Measures for Skewed Generalised Hyperbolic Family written by Katja Ignatieva and published by . This book was released on 2017 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper deals with the estimation of loss severity distribution arising from the historical data on univariate and multivariate losses. We present an innovative theoretical framework where the closed-form expression for the tail conditional expectation (TCE) is derived for the skewed general hyperbolic (GH) family of distributions. Skewed GH family is especially suitable for right-skewed positive random variables such as insurance losses. It allows to capture the asymmetry in the distribution of losses that tends to have a heavy right tail. As opposed to a widely used Value-at-Risk, TCE is a coherent risk measure, which takes into account the expected loss in the tail of the distribution. Our theoretical TCE results are verified for different distributions from the skewed GH family including its general cases: Student-t, variance gamma, normal inverse gaussian and hyperbolic distributions. GH family and its special cases turn out to provide excellent fit to univariate and multivariate data on Danish fire losses. TCE risk measure computed for the skewed family of GH distributions provides conservative estimators of risk, addressing the main challenge faced by insurance companies on how to reliably quantify the risk arising from the loss distribution. We extend our analysis to the multivariate framework when modelling portfolio of losses, allowing multivariate GH distribution to capture the combination of correlated risks and demonstrate how TCE of the portfolio can be decomposed into individual components, representing individual risk in the aggregate (portfolio) loss.
Author : Steven Kou
Publisher :
ISBN 13 :
Total Pages : 51 pages
Book Rating : 4.:/5 (13 download)
Download or read book On the Measurement of Economic Tail Risk written by Steven Kou and published by . This book was released on 2015 with total page 51 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper attempts to provide a decision-theoretic foundation for the measurement of economic tail risk, which is not only closely related to utility theory but also relevant to statistical model uncertainty. The main result is that the only risk measures that satisfy a set of economic axioms for the Choquet expected utility and the statistical property of elicitability (i.e. there exists an objective function such that minimizing the expected objective function yields the risk measure) are the mean functional and the median shortfall, which is the median of tail loss distribution. Elicitability is important for backtesting. We also extend the result to address model uncertainty by incorporating multiple scenarios. As an application, we argue that median shortfall is a better alternative than expected shortfall for setting capital requirements in Basel Accords.
Author : Carlos G. Pedraz
Publisher :
ISBN 13 :
Total Pages : 38 pages
Book Rating : 4.:/5 (13 download)
Download or read book Tail Risk in Energy Portfolios written by Carlos G. Pedraz and published by . This book was released on 2014 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: This article analyzes the tail behavior of energy price risk using a multivariate approach, in which the exposure to energy markets is given by a portfolio of oil, gas, coal, and electricity. To accommodate various dependence and tail decay patterns, this study models energy returns using different generalized hyperbolic conditional distributions and time-varying conditional mean and covariance.Employing daily energy futures data from August 2005 to March 2012, the authors recursively estimate the models and evaluate tail risk measures for the portfolio's profit-and-loss distribution for long and short positions at various horizons and confidence levels. Both in-sample and out-of-sample analysis applied to different energy portfolios show the importance of heavy tails and positive asymmetry in the distribution of energy risk factors. Thus, tail risk measures for energy portfolios based on standard methods (e.g. normality, constant covariance matrix) and on models with exponential tail decay underestimate actual tail risk, especially for short positions and short time horizons.
Author : Jon Danielsson
Publisher : John Wiley & Sons
ISBN 13 : 1119977118
Total Pages : 307 pages
Book Rating : 4.1/5 (199 download)
Download or read book Financial Risk Forecasting written by Jon Danielsson and published by John Wiley & Sons. This book was released on 2011-04-20 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Svetlozar T. Rachev
Publisher : John Wiley & Sons
ISBN 13 : 0471758906
Total Pages : 385 pages
Book Rating : 4.4/5 (717 download)
Download or read book Fat-Tailed and Skewed Asset Return Distributions written by Svetlozar T. Rachev and published by John Wiley & Sons. This book was released on 2005-09-15 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: While mainstream financial theories and applications assume that asset returns are normally distributed, overwhelming empirical evidence shows otherwise. Yet many professionals don’t appreciate the highly statistical models that take this empirical evidence into consideration. Fat-Tailed and Skewed Asset Return Distributions examines this dilemma and offers readers a less technical look at how portfolio selection, risk management, and option pricing modeling should and can be undertaken when the assumption of a non-normal distribution for asset returns is violated. Topics covered in this comprehensive book include an extensive discussion of probability distributions, estimating probability distributions, portfolio selection, alternative risk measures, and much more. Fat-Tailed and Skewed Asset Return Distributions provides a bridge between the highly technical theory of statistical distributional analysis, stochastic processes, and econometrics of financial returns and real-world risk management and investments.
Author : Woon K. Wong
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)
Download or read book Capturing Tail Risks Beyond VaR. written by Woon K. Wong and published by . This book was released on 2009 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since Value-at-Risk (VaR) disregards tail losses beyond the VaR boundary, the expected shortfall (ES), which measures the average loss when a VaR is exceeded, and the tail-risk-of-VaR (TR), which sums the sizes of tail losses, are used to investigate risks at the tails of distributions for major stock markets. As VaR exceptions are rare, we employ the saddlepoint or small sample asymptotic technique to backtest ES and TR. Because the two risk measures are complementary to each other and hence provide more powerful backtests, we are able to show that (a) the correct specification of distribution tail, rather than heteroscedastic process, plays a key role to accurate risk forecasts; and (b) it is best to model the tails separately from the central part of distribution using the generalized Pareto distribution. To sum up, we provide empirical evidence that financial markets behave differently during crises, and extreme risks cannot be modeled effectively under normal market conditions or based on a short data history.
Author : Bernhard Höfler
Publisher : GRIN Verlag
ISBN 13 : 363888273X
Total Pages : 89 pages
Book Rating : 4.6/5 (388 download)
Download or read book Risk Measures - Value at Risk and Beyond written by Bernhard Höfler and published by GRIN Verlag. This book was released on 2008 with total page 89 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Author : Kabir Dutta
Publisher :
ISBN 13 :
Total Pages : 93 pages
Book Rating : 4.:/5 (129 download)
Download or read book A Tale of Tails written by Kabir Dutta and published by . This book was released on 2007 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt: Operational risk is being recognized as an important risk component for financial institutions as evinced by the large sums of capital that are allocated to mitigate this risk. Therefore, risk measurement is of paramount concern for the purposes of capital allocation, hedging, and new product development for risk mitigation. We perform a comprehensive evaluation of commonly used methods and introduce new techniques to measure this risk with respect to various criteria. We find that our newly introduced techniques perform consistently better than the other models we tested.
Author : Srichander Ramaswamy
Publisher : John Wiley & Sons
ISBN 13 : 0471488321
Total Pages : 256 pages
Book Rating : 4.4/5 (714 download)
Download or read book Managing Credit Risk in Corporate Bond Portfolios written by Srichander Ramaswamy and published by John Wiley & Sons. This book was released on 2004-03-29 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Expert guidance on managing credit risk in bond portfolios Managing Credit Risk in Corporate Bond Portfolios shows readers howto measure and manage the risks of a corporate bond portfolioagainst its benchmark. This comprehensive guide explores a widerange of topics surrounding credit risk and bond portfolios,including the similarities and differences between corporate andgovernment bond portfolios, yield curve risk, default and creditmigration risk, Monte Carlo simulation techniques, and portfolioselection methods. Srichander Ramaswamy, PhD (Basel, Switzerland), is Head ofInvestment Analysis at the Bank for International Settlements (BIS)in Basel, Switzerland, and Adjunct Professor of Banking andFinance, University of Lausanne.
Author : Simona Roccioletti
Publisher : Springer
ISBN 13 : 365811908X
Total Pages : 155 pages
Book Rating : 4.6/5 (581 download)
Download or read book Backtesting Value at Risk and Expected Shortfall written by Simona Roccioletti and published by Springer. This book was released on 2015-12-04 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Gareth W. Peters
Publisher : John Wiley & Sons
ISBN 13 : 1118909550
Total Pages : 656 pages
Book Rating : 4.1/5 (189 download)
Download or read book Advances in Heavy Tailed Risk Modeling written by Gareth W. Peters and published by John Wiley & Sons. This book was released on 2015-05-05 with total page 656 pages. Available in PDF, EPUB and Kindle. Book excerpt: A cutting-edge guide for the theories, applications, and statistical methodologies essential to heavy tailed risk modeling Focusing on the quantitative aspects of heavy tailed loss processes in operational risk and relevant insurance analytics, Advances in Heavy Tailed Risk Modeling: A Handbook of Operational Risk presents comprehensive coverage of the latest research on the theories and applications in risk measurement and modeling techniques. Featuring a unique balance of mathematical and statistical perspectives, the handbook begins by introducing the motivation for heavy tailed risk processes in high consequence low frequency loss modeling. With a companion, Fundamental Aspects of Operational Risk and Insurance Analytics: A Handbook of Operational Risk, the book provides a complete framework for all aspects of operational risk management and includes: Clear coverage on advanced topics such as splice loss models, extreme value theory, heavy tailed closed form loss distributional approach models, flexible heavy tailed risk models, risk measures, and higher order asymptotic approximations of risk measures for capital estimation An exploration of the characterization and estimation of risk and insurance modelling, which includes sub-exponential models, alpha-stable models, and tempered alpha stable models An extended discussion of the core concepts of risk measurement and capital estimation as well as the details on numerical approaches to evaluation of heavy tailed loss process model capital estimates Numerous detailed examples of real-world methods and practices of operational risk modeling used by both financial and non-financial institutions Advances in Heavy Tailed Risk Modeling: A Handbook of Operational Risk is an excellent reference for risk management practitioners, quantitative analysts, financial engineers, and risk managers. The book is also a useful handbook for graduate-level courses on heavy tailed processes, advanced risk management, and actuarial science.
Author : Mr.Nassim N. Taleb
Publisher : International Monetary Fund
ISBN 13 : 1475505663
Total Pages : 24 pages
Book Rating : 4.4/5 (755 download)
Download or read book A New Heuristic Measure of Fragility and Tail Risks written by Mr.Nassim N. Taleb and published by International Monetary Fund. This book was released on 2012-08-01 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper presents a simple heuristic measure of tail risk, which is applied to individual bank stress tests and to public debt. Stress testing can be seen as a first order test of the level of potential negative outcomes in response to tail shocks. However, the results of stress testing can be misleading in the presence of model error and the uncertainty attending parameters and their estimation. The heuristic can be seen as a second order stress test to detect nonlinearities in the tails that can lead to fragility, i.e., provide additional information on the robustness of stress tests. It also shows how the measure can be used to assess the robustness of public debt forecasts, an important issue in many countries. The heuristic measure outlined here can be used in a variety of situations to ascertain an ordinal ranking of fragility to tail risks.
Author : Katja Ignatieva
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)
Download or read book Estimating the Tails of Loss Severity Via Conditional Risk Measures for the Family of Symmetric Generalised Hyperbolic Family written by Katja Ignatieva and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper addresses one of the main challenges faced by insurance companies and risk management departments, namely, how to develop standardised framework for measuring risks of underlying portfolios and in particular, how to most reliably estimate loss severity distribution from historical data. This paper investigates tail conditional expectation (TCE) and tail variance premium (TVP) risk measures for the family of symmetric generalised hyperbolic (SGH) distributions. In contrast to a widely used Value-at-Risk (VaR) measure, TCE satisfies the requirement of the "coherent" risk measure taking into account the expected loss in the tail of the distribution while TVP incorporates variability in the tail, providing the most conservative estimator of risk. We examine various distributions from the class of SGH distributions, which turn out to fit well financial data returns and allow for explicit formulas for TCE and TVP risk measures. In parallel, we obtain asymptotic behaviour for TCE and TVP risk measures for large quantile levels. Furthermore, we extend our analysis to the multivariate framework, allowing multivariate distri- butions to model combinations of correlated risks, and demonstrate how TCE can be decomposed into individual components, representing contribution of individual risks to the aggregate portfolio risk.
Author : Andrew Rozanov
Publisher :
ISBN 13 : 9781782720805
Total Pages : 304 pages
Book Rating : 4.7/5 (28 download)
Download or read book Tail Risk Hedging written by Andrew Rozanov and published by . This book was released on 2014 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Carlos Pedro dos Santos Gonçalves
Publisher :
ISBN 13 :
Total Pages : 29 pages
Book Rating : 4.:/5 (129 download)
Download or read book Tail Risk and Pk-Tail Risk written by Carlos Pedro dos Santos Gonçalves and published by . This book was released on 2005 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper discusses the notion of tail risk, and the ability of a tail risk measure to reflect this kind of risk. In particular, Yamai and Yoshiba's (2001, 2002) notion of strict risk measure tail risk is discussed and linked with a different notion of tail risk, the pK-tail risk, which is the risk associated with the probability measure conditional on the event that the losses are at least as large as K. A subset of pK-tail risk measures that are free of strict risk measure tail risk is introduced. These notions are then extended to Yaari's (1987) dual theory and the distorted risk measures framework.
Author : Woon K. Wong
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)
Download or read book Backtesting Value-at-Risk Based on Tail Losses written by Woon K. Wong and published by . This book was released on 2008 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Extreme losses caused by leverage and financial derivatives highlight the need to backtest Value-at-Risk (VaR) based on sizes of tail losses, for the risk measure disregards losses beyond the VaR boundary and there is no formal statistical analysis required for stress testing. While Basel II backtests VaR by counting the number of exceptions, this paper proposes to use saddlepoint technique to backtest VaR by summing the tail losses. Monte Carlo simulations show that the technique is very accurate and powerful even for small samples. The proposed backtest finds substantial downside tail risks in S&P 500, and that risk models which account for jumps, skewed and fat-tailed distributions fail to capture the tail risk during the 1987 stock market crash. Finally, the saddlepoint technique is used to derive a multiplication factor for risk capital requirement that is responsive to sizes of tail losses.
