Conditional Value-at-Risk for Log-Distributions PDF Download

Author: Valentyn Khokhlov
Publisher:
ISBN:
Category :
Languages : en
Pages : 10

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Book Description
Conditional Value-at-Risk (CVaR) represents a significant improvement over the Value-at-Risk (VaR) in the area of risk measurement, as it catches the risk beyond the VaR threshold. CVaR is also theoretically more solid, being a coherent risk measure, which enables building more robust risk assessment and management systems. This paper addresses the derivation of the closed-form CVaR formulas for log-normal, log-logistic, log-Laplace and log-hyperbolic secant distributions, which are relevant for modeling the returns of financial assets. In many cases financial risk managers assume that not the returns themselves but their logarithms adhere to a particular distribution, and the samples of log-returns are considered. In such cases, the appropriate way to assess risk would be to use a log-distribution for CVaR and VaR estimation. We show how to use the log-normal and the log-logistic distributions for assessing the risk for different asset classes in 2003-2007 and 2007-2009. The log-Laplace and the log-hyperbolic secant distributions have fatter tails, and they may provide a higher accuracy for the tail risk assessment during the crisis periods.

Author: Saul I. Gass
Publisher: Springer Science & Business Media
ISBN: 1461304598
Category : Business & Economics
Languages : en
Pages : 774

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Operations Research: 1934-1941," 35, 1, 143-152; "British The goal of the Encyclopedia of Operations Research and Operational Research in World War II," 35, 3, 453-470; Management Science is to provide to decision makers and "U. S. Operations Research in World War II," 35, 6, 910-925; problem solvers in business, industry, government and and the 1984 article by Harold Lardner that appeared in academia a comprehensive overview of the wide range of Operations Research: "The Origin of Operational Research," ideas, methodologies, and synergistic forces that combine to 32, 2, 465-475. form the preeminent decision-aiding fields of operations re search and management science (OR/MS). To this end, we The Encyclopedia contains no entries that define the fields enlisted a distinguished international group of academics of operations research and management science. OR and MS and practitioners to contribute articles on subjects for are often equated to one another. If one defines them by the which they are renowned. methodologies they employ, the equation would probably The editors, working with the Encyclopedia's Editorial stand inspection. If one defines them by their historical Advisory Board, surveyed and divided OR/MS into specific developments and the classes of problems they encompass, topics that collectively encompass the foundations, applica the equation becomes fuzzy. The formalism OR grew out of tions, and emerging elements of this ever-changing field. We the operational problems of the British and U. s. military also wanted to establish the close associations that OR/MS efforts in World War II.

Author: R. Tyrrell Rockafellar
Publisher:
ISBN:
Category :
Languages : en
Pages : 0

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Author: Valentyn Khokhlov
Publisher:
ISBN:
Category :
Languages : en
Pages : 11

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Book Description
Conditional Value-at-Risk (CVaR) represents a significant improvement over the Value-at-Risk (VaR) in the area of risk measurement, as it catches the risk beyond the VaR threshold. CVaR is also theoretically more solid, being a coherent risk measure, which enables building more robust risk assessment and management systems. However, in its general form CVaR calculations require sophisticated mathematical software, whereas VaR can be easily calculated using spreadsheets. In this paper closed-form CVaR formulas are derived for the most important elliptical distributions, such as normal, Student's t-distribution, Laplace and logistic distributions. These closed-form formulas not only enable practitioners to estimate CVaR in spreadsheets, but also allow developing portfolio optimization models by providing closed-form objective functions for them. The results of variance-covariance CVaR estimation were compared with the historical CVaR, and the relative estimation error is between 6% and 10%, which is comparable with VaR estimation error.

Author: M. A. H. Dempster
Publisher: Cambridge University Press
ISBN: 1139437496
Category : Mathematics
Languages : en
Pages : 290

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Book Description
The use of derivative products in risk management has spread from commodities, stocks and fixed income items, to such virtual commodities as energy, weather and bandwidth. All this can give rise to so-called volatility and there has been a consequent development in formal risk management techniques to cover all types of risk: market, credit, liquidity, etc. One of these techniques, Value at Risk, was developed specifically to help manage market risk over short periods. Its success led, somewhat controversially, to its take up and extension to credit risk over longer time-scales. This extension, ultimately not successful, led to the collapse of a number of institutions. The present book, which was originally published in 2002, by some of the leading figures in risk management, examines the complex issues that concern the stability of the global financial system by presenting a mix of theory and practice.

Author: Angelo Corelli
Publisher: Emerald Group Publishing
ISBN: 1789737931
Category : Business & Economics
Languages : en
Pages : 626

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Book Description
Understanding Financial Risk Management provides an innovative approach to financial risk management. With a broad view of theory and the industry, it aims at being a friendly, but serious, starting point for those who encounter risk management for the first time, as well as for more advanced users.

Author: Lukasz Snopek
Publisher: John Wiley & Sons
ISBN: 111997688X
Category : Business & Economics
Languages : en
Pages : 325

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Book Description
In the wake of the recent financial crisis, many will agree that it is time for a fresh approach to portfolio management. The Complete Guide to Portfolio Construction and Management provides practical investment advice for building a robust, diversified portfolio. Written by a high-profile investment adviser, this book reveals a practical portfolio management framework and new approach to portfolio construction based on four key market forces: macro, fundamental, technical, and behavioural. It is an insight that takes the focus off numbers, looking instead at the role of risk and behavior in finance. As we have seen with the recent finance meltdown, traditional portfolio management techniques are flawed. Investors need to understand those flaws and learn how to incorporate risk management and behavioral finance into their asset management strategies. With a foreword by industry leader Francois-Serge L'habitant, this is your one-stop guide, with new ways for you to manage, grow and preserve your investment portfolio, even in uncertain markets.

Author: Paul Embrechts
Publisher: Springer Science & Business Media
ISBN: 3642334830
Category : Business & Economics
Languages : en
Pages : 657

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Book Description
"A reader's first impression on leafing through this book is of the large number of graphs and diagrams, used to illustrate shapes of distributions...and to show real data examples in various ways. A closer reading reveals a nice mix of theory and applications, with the copious graphical illustrations alluded to. Such a mixture is of course dear to the heart of the applied probabilist/statistician, and should impress even the most ardent theorists." --MATHEMATICAL REVIEWS

Author: Carol Alexander
Publisher: John Wiley & Sons
ISBN: 0470997885
Category : Business & Economics
Languages : en
Pages : 503

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Book Description
Written by leading market risk academic, Professor Carol Alexander, Value-at-Risk Models forms part four of the Market Risk Analysis four volume set. Building on the three previous volumes this book provides by far the most comprehensive, rigorous and detailed treatment of market VaR models. It rests on the basic knowledge of financial mathematics and statistics gained from Volume I, of factor models, principal component analysis, statistical models of volatility and correlation and copulas from Volume II and, from Volume III, knowledge of pricing and hedging financial instruments and of mapping portfolios of similar instruments to risk factors. A unifying characteristic of the series is the pedagogical approach to practical examples that are relevant to market risk analysis in practice. All together, the Market Risk Analysis four volume set illustrates virtually every concept or formula with a practical, numerical example or a longer, empirical case study. Across all four volumes there are approximately 300 numerical and empirical examples, 400 graphs and figures and 30 case studies many of which are contained in interactive Excel spreadsheets available from the the accompanying CD-ROM . Empirical examples and case studies specific to this volume include: Parametric linear value at risk (VaR)models: normal, Student t and normal mixture and their expected tail loss (ETL); New formulae for VaR based on autocorrelated returns; Historical simulation VaR models: how to scale historical VaR and volatility adjusted historical VaR; Monte Carlo simulation VaR models based on multivariate normal and Student t distributions, and based on copulas; Examples and case studies of numerous applications to interest rate sensitive, equity, commodity and international portfolios; Decomposition of systematic VaR of large portfolios into standard alone and marginal VaR components; Backtesting and the assessment of risk model risk; Hypothetical factor push and historical stress tests, and stress testing based on VaR and ETL.

Author: Kevin Dowd
Publisher: John Wiley & Sons
ISBN: 0470855215
Category : Business & Economics
Languages : en
Pages : 395

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Book Description
The most up-to-date resource on market risk methodologies Financial professionals in both the front and back office require an understanding of market risk and how to manage it. Measuring Market Risk provides this understanding with an overview of the most recent innovations in Value at Risk (VaR) and Expected Tail Loss (ETL) estimation. This book is filled with clear and accessible explanations of complex issues that arise in risk measuring-from parametric versus nonparametric estimation to incre-mental and component risks. Measuring Market Risk also includes accompanying software written in Matlab—allowing the reader to simulate and run the examples in the book.