Download or read book A Theory for Measures of Tail Risk written by Fangda Liu and published by . This book was released on 2020 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: The notion of "tail risk" has been a crucial consideration in modern risk management. To achieve a comprehensive understanding of the tail risk, we carry out an axiomatic study for risk measures which quantify the tail risk, that is, the behavior of a risk beyond a certain quantile. Such risk measures are referred to as tail risk measures in this paper. The two popular classes of regulatory risk measures in banking and insurance, the Value-at-Risk (VaR) and the Expected Shortfall (ES), are prominent, yet elementary, examples of tail risk measures. We establish a connection between a tail risk measure and a corresponding law-invariant risk measure, called its generator, and investigate their joint properties. A tail risk measure inherits many properties from its generator, but not subadditivity or convexity; nevertheless, a tail risk measure is coherent if and only if its generator is coherent. We explore further relevant issues on tail risk measures, such as bounds, distortion risk measures, risk aggregation, elicitability, and dual representations. In particular, there is no elicitable tail convex risk measure rather than the essential supremum, and under a continuity condition, the only elicitable and positively homogeneous monetary tail risk measures are the VaRs.
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.
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.
Download or read book How the Risk Measures Play Important Roles for Tail Risk Management and Diversification written by Takuo Higashide and published by . This book was released on 2019 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the world of investment, the subject of building a portfolio concerning tail risk is still one of the frequently discussed subjects and unquestionably vital for investors. This paper seeks to examine how the risk measures, lower tail-dependence based on the copulas approach and Conditional Value-at-Risk (CVaR), affect the portfolio strategies and play important roles for tail risk management and diversify the portfolio. By using these two risk measures mentioned above, two different types of risk-based portfolios are proposed that consider for the tail risks: 1) Minimum-lower tail-dependence portfolio (RMTP) and 2) Risk Parity Portfolio based on Conditional Value-at-Risk (CRPP). The simulation results showed how those two risk-based portfolios, RMTP and CRPP, work effectively in multi-asset allocation framework with 6 assets: stocks and sovereign bonds of Japan, United States and Germany, based on the monthly rebalance rule, using 2004-2018 sample period. One of the key findings were that both RMTP and CRPP strategies delivered better performances compared with the traditional portfolio strategies in terms of sharp ratio: 1) RMTP yielded 0.92 and 2) CRPP yielded 0.99 (by adding an appropriate risk reduction to this portfolio, the sharp ratio went up to 1.76). In addition, both of these two strategies also worked effectively in terms of the average of maximum monthly drawdown related to the effect of the tail risk: 1) RMTP by 1.80% and 2) CRPP by 1.74% (by adding an appropriate risk reduction to this portfolio, maximum drawdown decreased to 0.78%). Furthermore, this paper also studies an enhancement strategy based on Risk Parity Portfolios (RPP) focusing on and using co-integration relationship (co-integration approach). According to the simulation result, this proposed enhancement strategy has a potential to yield roughly 4.5% return. Finally, this paper presents the explicit derivation of lower tail-dependence and co-integration approach.
Download or read book Robust and Practical Estimation for Measures of Tail Risk written by Cristian Homescu and published by . This book was released on 2014 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt: We describe characteristics of various risk measures (Value-at-Risk, Expected Shortfall, etc.) that are used to analyze and quantify the tail risk exposure, and discuss their relative strengths and weaknesses. Emphasis is placed on presenting and comparing methodologies to compute and backtest estimates for these risk measures, from a practical perspective. We also consider the regulators' requirements regarding tail risk measures, especially in the framework provided by the most recent accords of the Basel Committee on Banking Regulation, known as Basel II, 2.5, and III.
Download or read book Extreme Value Theory for Tail related Risk Measures written by Evis Këllezi and published by . This book was released on 2000 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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:
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
Download or read book Tail Risk and Asset Prices written by Bryan Kelly and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose a new measure of time-varying tail risk that is directly estimable from the cross section of returns. We exploit firm-level price crashes every month to identify common fluctuations in tail risk across stocks. Our tail measure is significantly correlated with tail risk measures extracted from S&P 500 index options, but is available for a longer sample since it is calculated from equity data. We show that tail risk has strong predictive power for aggregate market returns: A one standard deviation increase in tail risk forecasts an increase in excess market returns of 4.5% over the following year. Cross-sectionally, stocks with high loadings on past tail risk earn an annual three-factor alpha 5.4% higher than stocks with low tail risk loadings. These findings are consistent with asset pricing theories that relate equity risk premia to rare disasters or other forms of tail risk.
Download or read book Tail Risk Killers How Math Indeterminacy and Hubris Distort Markets written by Jeffrey McGinn and published by McGraw Hill Professional. This book was released on 2012-01-06 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reshape your investing strategy for an increasingly uncertain world “An engrossing, fast-paced, terrific read for anyone interested in the financial imbalances due to too much reliance on math and too little respect for indeterminacy.” —Tyler Durden, ZeroHedge.com The world does not unfold according to a fixed set of rules. It is a dynamical system whose evolution looks like a bell curve with fat “tails.” The same is true of financial markets. However, every day we rely on the certainty and precision of mathematical strategies that assume the contrary to control and grow wealth in markets. Tail Risk Killers shows you how the rigidity of model-based thinking has led to the fragility of today’s global financial marketplace, and it explains how to use adaptive trading strategies to mitigate risk in impending market conditions. Risk management veteran Jeff McGinn pokes holes in prevalent assumptions about how financial markets act that tend to underestimate the likelihood of occurrence of extreme events. Through clear, conversational writing, real-world anecdotes, and easy-tofollow formulas, he provides a glimpse into the way tomorrow’s successful traders are viewing financial markets—with an eye for probability distributions. While illustrating how to protect your assets from tail risk, he shows you how to: Implement the six axioms for risk management Prepare for the unintended consequences of central banks suppressing tail risk Identify and avoid the dark risks hidden in today’s derivative-laden financial system Anticipate the fate of credit default swaps that may not face extinction McGinn argues that the intervention of central banks has robbed global markets of their opportunities to adapt, but this highly relevant book shows you that it is not too late to adapt your portfolio to survive the extreme events that happen more often than popular financial models suggest. Tail Risk Killers helps you discover useful information and processes beyond the focus of industry standards, helps you connect the dots of evolving trading strategies and time your next trade for maximum profitability.
Download or read book Tail Risk of Hedge Funds written by Gregor Aleksander Gawron and published by Cuvillier Verlag. This book was released on 2007 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Forward Looking Tail Risk Measures written by Markus Huggenberger and published by . This book was released on 2018 with total page 67 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present an analytical framework for the forward-looking measurement of extreme market risk. In contrast to standard techniques relying on past return data, we propose to extract Value-at-Risk and Expected Shortfall under the physical measure from current option prices. Our empirical evidence suggests that the resulting estimates accurately capture the tail risk of the S&P 500 and that they quickly react to changing market conditions. Compared to dynamic tail risk forecasts driven by past returns, our forward-looking estimates are relatively higher during good times and lower during adverse economic conditions, which could reduce the amplification effects of conventional dynamic risk management policies.
Download or read book Measuring the Tail Risk written by Alexandru Vali Asimit and published by . This book was released on 2017 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: The risk exposure of a business line could be perceived in many ways and is sensitive to the exercise that is performed. One way is to understand the effect of some common/reference risk over the performance of the business line in question, but irrespective of the modelling exercise, the exposure is evaluated under the presence of some suitable adverse scenarios. That is, measuring the tail risk is the main aim. We choose to evaluate the performance via an expectation, which is the most acceptable risk measure amongst academics, practitioners and regulators. In contrast to the common practice where the extreme region is chosen such that only the common/reference risk is explicitly allowed to be large, we assume in this paper an extreme region where both the business line in question and common/reference risks are explicitly allowed to be large. The advantage of this tail risk measure is that the asymptotic approximations are meaningful in all cases, especially in the asymptotic independence case, which helps in understanding the risk exposure in any possible setting. Our numerical examples illustrate these findings and provide a discussion about the sensitivity analysis of our approximations, which is a standard way of checking the importance of parameter estimation of the risk model. The numerical analysis shows strong evidence that our proposed tail risk measure has a lower sensitivity than the standard tail risk measure.
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:
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.
Download or read book Time Series Models written by D.R. Cox and published by CRC Press. This book was released on 2020-11-26 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: The analysis prediction and interpolation of economic and other time series has a long history and many applications. Major new developments are taking place, driven partly by the need to analyze financial data. The five papers in this book describe those new developments from various viewpoints and are intended to be an introduction accessible to readers from a range of backgrounds. The book arises out of the second Seminaire European de Statistique (SEMSTAT) held in Oxford in December 1994. This brought together young statisticians from across Europe, and a series of introductory lectures were given on topics at the forefront of current research activity. The lectures form the basis for the five papers contained in the book. The papers by Shephard and Johansen deal respectively with time series models for volatility, i.e. variance heterogeneity, and with cointegration. Clements and Hendry analyze the nature of prediction errors. A complementary review paper by Laird gives a biometrical view of the analysis of short time series. Finally Astrup and Nielsen give a mathematical introduction to the study of option pricing. Whilst the book draws its primary motivation from financial series and from multivariate econometric modelling, the applications are potentially much broader.
Download or read book Measurement of Tail Risk written by Marta Mylyan and published by . This book was released on 2014 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt:
