Risk Models and Their Estimation

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Publisher : ACTEX Publications
ISBN 13 : 1566987709
Total Pages : 1150 pages
Book Rating : 4.5/5 (669 download)

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Book Synopsis Risk Models and Their Estimation by : Stephen G. Kellison

Download or read book Risk Models and Their Estimation written by Stephen G. Kellison and published by ACTEX Publications. This book was released on 2011 with total page 1150 pages. Available in PDF, EPUB and Kindle. Book excerpt: Much of actuarial science deals with the analysis and management of financial risk. In this text we address the topic of loss models, traditionally called risk theory by actuaries, including the estimation of such models from sample data. The theory of survival models is addressed in other texts, including the ACTEX work entitled Models for Quantifying Risk which might be considered a companion text to this one. In Risk Models and Their Estimation we consider as well the estimation of survival models, in both tabular and parametric form, from sample data. This text is a valuable reference for those preparing for Exam C of the Society of Actuaries and Exam 4 of the Casualty Actuarial Society. A separate solutions' manual with detailed solutions to the text exercises is also available.

Financial Risk Management with Bayesian Estimation of GARCH Models

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Publisher : Springer Science & Business Media
ISBN 13 : 3540786570
Total Pages : 206 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Financial Risk Management with Bayesian Estimation of GARCH Models by : David Ardia

Download or read book Financial Risk Management with Bayesian Estimation of GARCH Models written by David Ardia and published by Springer Science & Business Media. This book was released on 2008-05-08 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents in detail methodologies for the Bayesian estimation of sing- regime and regime-switching GARCH models. These models are widespread and essential tools in n ancial econometrics and have, until recently, mainly been estimated using the classical Maximum Likelihood technique. As this study aims to demonstrate, the Bayesian approach o ers an attractive alternative which enables small sample results, robust estimation, model discrimination and probabilistic statements on nonlinear functions of the model parameters. The author is indebted to numerous individuals for help in the preparation of this study. Primarily, I owe a great debt to Prof. Dr. Philippe J. Deschamps who inspired me to study Bayesian econometrics, suggested the subject, guided me under his supervision and encouraged my research. I would also like to thank Prof. Dr. Martin Wallmeier and my colleagues of the Department of Quantitative Economics, in particular Michael Beer, Roberto Cerratti and Gilles Kaltenrieder, for their useful comments and discussions. I am very indebted to my friends Carlos Ord as Criado, Julien A. Straubhaar, J er ^ ome Ph. A. Taillard and Mathieu Vuilleumier, for their support in the elds of economics, mathematics and statistics. Thanks also to my friend Kevin Barnes who helped with my English in this work. Finally, I am greatly indebted to my parents and grandparents for their support and encouragement while I was struggling with the writing of this thesis.

Health Risks from Exposure to Low Levels of Ionizing Radiation

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Publisher : National Academies Press
ISBN 13 : 0309133343
Total Pages : 422 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Health Risks from Exposure to Low Levels of Ionizing Radiation by : Committee to Assess Health Risks from Exposure to Low Levels of Ionizing Radiation

Download or read book Health Risks from Exposure to Low Levels of Ionizing Radiation written by Committee to Assess Health Risks from Exposure to Low Levels of Ionizing Radiation and published by National Academies Press. This book was released on 2006-03-23 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the seventh in a series of titles from the National Research Council that addresses the effects of exposure to low dose LET (Linear Energy Transfer) ionizing radiation and human health. Updating information previously presented in the 1990 publication, Health Effects of Exposure to Low Levels of Ionizing Radiation: BEIR V, this book draws upon new data in both epidemiologic and experimental research. Ionizing radiation arises from both natural and man-made sources and at very high doses can produce damaging effects in human tissue that can be evident within days after exposure. However, it is the low-dose exposures that are the focus of this book. So-called “late” effects, such as cancer, are produced many years after the initial exposure. This book is among the first of its kind to include detailed risk estimates for cancer incidence in addition to cancer mortality. BEIR VII offers a full review of the available biological, biophysical, and epidemiological literature since the last BEIR report on the subject and develops the most up-to-date and comprehensive risk estimates for cancer and other health effects from exposure to low-level ionizing radiation.

Survival Models and Their Estimation

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Publisher :
ISBN 13 :
Total Pages : 348 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Survival Models and Their Estimation by : Dick London

Download or read book Survival Models and Their Estimation written by Dick London and published by . This book was released on 1988 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Validation of Risk Models

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Publisher : Springer
ISBN 13 : 1137436964
Total Pages : 242 pages
Book Rating : 4.1/5 (374 download)

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Book Synopsis The Validation of Risk Models by : S. Scandizzo

Download or read book The Validation of Risk Models written by S. Scandizzo and published by Springer. This book was released on 2016-07-01 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a one-stop-shop reference for risk management practitioners involved in the validation of risk models. It is a comprehensive manual about the tools, techniques and processes to be followed, focused on all the models that are relevant in the capital requirements and supervisory review of large international banks.

Quantitative Operational Risk Models

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Publisher : CRC Press
ISBN 13 : 1439895937
Total Pages : 236 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Quantitative Operational Risk Models by : Catalina Bolance

Download or read book Quantitative Operational Risk Models written by Catalina Bolance and published by CRC Press. This book was released on 2012-02-15 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using real-life examples from the banking and insurance industries, Quantitative Operational Risk Models details how internal data can be improved based on external information of various kinds. Using a simple and intuitive methodology based on classical transformation methods, the book includes real-life examples of the combination of internal dat

Advances in Heavy Tailed Risk Modeling

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Publisher : John Wiley & Sons
ISBN 13 : 1118909542
Total Pages : 1235 pages
Book Rating : 4.1/5 (189 download)

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Book Synopsis Advances in Heavy Tailed Risk Modeling by : Gareth W. Peters

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 2015-05-21 with total page 1235 pages. Available in PDF, EPUB and Kindle. Book excerpt: ADVANCES IN HEAVY TAILED RISK MODELING 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. A companion with Fundamental Aspects of Operational Risk and Insurance Analytics: A Handbook of Operational Risk, the handbook 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 distribution 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 modeling, 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 handbook is also useful for graduate-level courses on heavy tailed processes, advanced risk management, and actuarial science.

Market Risk Analysis, Value at Risk Models

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Publisher : John Wiley & Sons
ISBN 13 : 0470997885
Total Pages : 503 pages
Book Rating : 4.4/5 (79 download)

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Book Synopsis Market Risk Analysis, Value at Risk Models by : Carol Alexander

Download or read book Market Risk Analysis, Value at Risk Models written by Carol Alexander and published by John Wiley & Sons. This book was released on 2009-02-09 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Financial Risk Forecasting

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Publisher : John Wiley & Sons
ISBN 13 : 1119977118
Total Pages : 307 pages
Book Rating : 4.1/5 (199 download)

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Book Synopsis Financial Risk Forecasting by : Jon Danielsson

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.

The Basel II Risk Parameters

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Publisher : Springer Science & Business Media
ISBN 13 : 3642161146
Total Pages : 432 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis The Basel II Risk Parameters by : Bernd Engelmann

Download or read book The Basel II Risk Parameters written by Bernd Engelmann and published by Springer Science & Business Media. This book was released on 2011-03-31 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: The estimation and the validation of the Basel II risk parameters PD (default probability), LGD (loss given fault), and EAD (exposure at default) is an important problem in banking practice. These parameters are used on the one hand as inputs to credit portfolio models and in loan pricing frameworks, on the other to compute regulatory capital according to the new Basel rules. This book covers the state-of-the-art in designing and validating rating systems and default probability estimations. Furthermore, it presents techniques to estimate LGD and EAD and includes a chapter on stress testing of the Basel II risk parameters. The second edition is extended by three chapters explaining how the Basel II risk parameters can be used for building a framework for risk-adjusted pricing and risk management of loans.

Models for Quantifying Risk, Sixth Edition

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Publisher : ACTEX Publications
ISBN 13 : 1625423470
Total Pages : 538 pages
Book Rating : 4.6/5 (254 download)

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Book Synopsis Models for Quantifying Risk, Sixth Edition by : Stephen J. Camilli, ASA

Download or read book Models for Quantifying Risk, Sixth Edition written by Stephen J. Camilli, ASA and published by ACTEX Publications. This book was released on 2014-06-24 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is used in many university courses for SOA Exam MLC preparation. The Fifth Edition is the official reference for CAS Exam LC. The Sixth Edition of this textbook presents a variety of stochastic models for the actuary to use in undertaking the analysis of risk. It is designed to be appropriate for use in a two or three semester university course in basic actuarial science. It was written with the SOA Exam MLC and CAS Exam LC in mind. Models are evaluated in a generic form with life contingencies included as one of many applications of the science. Students will find this book to be a valuable reference due to its easy-to-understand explanations and end-of-chapter exercises. In 2013 the Society of Actuaries announced a change to Exam MLC's format, incorporating 60% written answer questions and new standard notation and terminology to be used for the exam. There are several areas of expanded content in the Sixth Edition due to these changes. Six important changes to the Sixth Edition: WRITTEN-ANSWER EXAMPLES This edition offers additional written-answer examples in order to better prepare the reader for the new SOA eam format. NOTATION AND TERMINOLOGY CONFORMS TO EXAM MLC MQR 6 fully incorporates all standard notation and terminology for exam MLC, as detailed by the SOA in their document Notation and Terminology Used on Exam MLC. MULTI-STATE MODELS Extension of multi-state model representationt to almost all topics covered in the text. FOCUS ON NORTH AMERICAN MARKET AND ACTUARIAL PROFESSION This book is written specifically for the multi-disciplinary needs of the North American Market. This is reflected in both content and terminology. PROFIT TESTING, PARTICIPATING INSURANCE, AND UNIVERSAL LIFE MQR 6 contains an expanded treatment of these topics. THIELE'S EQUATION Additional applications of this important equation are presented, to more fully prepare the reader for exam day. A separate solutions manual with detailed solutions to all of the text exercises is also available. Please see the Related Items Tab for a direct link I selected Models for Quantifying Risk as the text for my class. Given that the syllabus had changed quite dramatically from prior years, I was looking for a text that would cover all the material in the new syllabus in a way that was rigorous, easy to understand, and would prepare students for the May 2012 MLC exam. To me, the text with the accompanying solutions manual does precisely that. --Jay Vadiveloo, Ph.D., FSA, MAAA, CFA, Math Department, University of Connecticut I found that the exposition of the material is thorough while the concepts are readily accessible and well illustrated with examples. The book was an invaluable source of practice problems when I was preparing for the Exam MLC. Studying from it enabled me to pass this exam." -- Dmitry Glotov, Math Department, University of Connecticut "This book is extremely well written and structured." -- Kate Li, Student, University of Connecticut "Overall, the text is thorough, understandable, and well-organized. The clear exposition and excellent use of examples will benefit the student and help her avoid 'missing the forest for the trees'. I was impressed by the quality and quantity of examples and exercises throughout the text; students will find this collection of problems sorted by topic valuable for their exam preparation. Overall, I strongly recommend the book." -- Kristin Moore, Ph.D., ASA, University of Michigan

Credit Risk Modeling

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Publisher : Princeton University Press
ISBN 13 : 1400829194
Total Pages : 328 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Credit Risk Modeling by : David Lando

Download or read book Credit Risk Modeling written by David Lando and published by Princeton University Press. This book was released on 2009-12-13 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: Credit risk is today one of the most intensely studied topics in quantitative finance. This book provides an introduction and overview for readers who seek an up-to-date reference to the central problems of the field and to the tools currently used to analyze them. The book is aimed at researchers and students in finance, at quantitative analysts in banks and other financial institutions, and at regulators interested in the modeling aspects of credit risk. David Lando considers the two broad approaches to credit risk analysis: that based on classical option pricing models on the one hand, and on a direct modeling of the default probability of issuers on the other. He offers insights that can be drawn from each approach and demonstrates that the distinction between the two approaches is not at all clear-cut. The book strikes a fruitful balance between quickly presenting the basic ideas of the models and offering enough detail so readers can derive and implement the models themselves. The discussion of the models and their limitations and five technical appendixes help readers expand and generalize the models themselves or to understand existing generalizations. The book emphasizes models for pricing as well as statistical techniques for estimating their parameters. Applications include rating-based modeling, modeling of dependent defaults, swap- and corporate-yield curve dynamics, credit default swaps, and collateralized debt obligations.

Credit Risk Analytics

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Publisher : John Wiley & Sons
ISBN 13 : 1119143985
Total Pages : 517 pages
Book Rating : 4.1/5 (191 download)

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Book Synopsis Credit Risk Analytics by : Bart Baesens

Download or read book Credit Risk Analytics written by Bart Baesens and published by John Wiley & Sons. This book was released on 2016-10-03 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: The long-awaited, comprehensive guide to practical credit risk modeling Credit Risk Analytics provides a targeted training guide for risk managers looking to efficiently build or validate in-house models for credit risk management. Combining theory with practice, this book walks you through the fundamentals of credit risk management and shows you how to implement these concepts using the SAS credit risk management program, with helpful code provided. Coverage includes data analysis and preprocessing, credit scoring; PD and LGD estimation and forecasting, low default portfolios, correlation modeling and estimation, validation, implementation of prudential regulation, stress testing of existing modeling concepts, and more, to provide a one-stop tutorial and reference for credit risk analytics. The companion website offers examples of both real and simulated credit portfolio data to help you more easily implement the concepts discussed, and the expert author team provides practical insight on this real-world intersection of finance, statistics, and analytics. SAS is the preferred software for credit risk modeling due to its functionality and ability to process large amounts of data. This book shows you how to exploit the capabilities of this high-powered package to create clean, accurate credit risk management models. Understand the general concepts of credit risk management Validate and stress-test existing models Access working examples based on both real and simulated data Learn useful code for implementing and validating models in SAS Despite the high demand for in-house models, there is little comprehensive training available; practitioners are left to comb through piece-meal resources, executive training courses, and consultancies to cobble together the information they need. This book ends the search by providing a comprehensive, focused resource backed by expert guidance. Credit Risk Analytics is the reference every risk manager needs to streamline the modeling process.

Ruin Probabilities

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Author :
Publisher : Elsevier
ISBN 13 : 0081020988
Total Pages : 276 pages
Book Rating : 4.0/5 (81 download)

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Book Synopsis Ruin Probabilities by : Yuliya Mishura

Download or read book Ruin Probabilities written by Yuliya Mishura and published by Elsevier. This book was released on 2016-11-08 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ruin Probabilities: Smoothness, Bounds, Supermartingale Approach deals with continuous-time risk models and covers several aspects of risk theory. The first of them is the smoothness of the survival probabilities. In particular, the book provides a detailed investigation of the continuity and differentiability of the infinite-horizon and finite-horizon survival probabilities for different risk models. Next, it gives some possible applications of the results concerning the smoothness of the survival probabilities. Additionally, the book introduces the supermartingale approach, which generalizes the martingale one introduced by Gerber, to get upper exponential bounds for the infinite-horizon ruin probabilities in some generalizations of the classical risk model with risky investments. Provides new original results Detailed investigation of the continuity and differentiability of the infinite-horizon and finite-horizon survival probabilities, as well as possible applications of these results An excellent supplement to current textbooks and monographs in risk theory Contains a comprehensive list of useful references

Radiation Risk Estimation

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Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110433664
Total Pages : 270 pages
Book Rating : 4.1/5 (14 download)

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Book Synopsis Radiation Risk Estimation by : Sergii Masiuk

Download or read book Radiation Risk Estimation written by Sergii Masiuk and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-03-06 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph discusses statistics and risk estimates applied to radiation damage under the presence of measurement errors. The first part covers nonlinear measurement error models, with a particular emphasis on efficiency of regression parameter estimators. In the second part, risk estimation in models with measurement errors is considered. Efficiency of the methods presented is verified using data from radio-epidemiological studies. Contents: Part I - Estimation in regression models with errors in covariates Measurement error models Linear models with classical error Polynomial regression with known variance of classical error Nonlinear and generalized linear models Part II Radiation risk estimation under uncertainty in exposure doses Overview of risk models realized in program package EPICURE Estimation of radiation risk under classical or Berkson multiplicative error in exposure doses Radiation risk estimation for persons exposed by radioiodine as a result of the Chornobyl accident Elements of estimating equations theory Consistency of efficient methods Efficient SIMEX method as a combination of the SIMEX method and the corrected score method Application of regression calibration in the model with additive error in exposure doses

Credit Risk Modeling using Excel and VBA

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Publisher : John Wiley & Sons
ISBN 13 : 0470660929
Total Pages : 372 pages
Book Rating : 4.4/5 (76 download)

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Book Synopsis Credit Risk Modeling using Excel and VBA by : Gunter Löeffler

Download or read book Credit Risk Modeling using Excel and VBA written by Gunter Löeffler and published by John Wiley & Sons. This book was released on 2011-01-31 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is common to blame the inadequacy of credit risk models for the fact that the financial crisis has caught many market participants by surprise. On closer inspection, though, it often appears that market participants failed to understand or to use the models correctly. The recent events therefore do not invalidate traditional credit risk modeling as described in the first edition of the book. A second edition is timely, however, because the first dealt relatively briefly with instruments featuring prominently in the crisis (CDSs and CDOs). In addition to expanding the coverage of these instruments, the book will focus on modeling aspects which were of particular relevance in the financial crisis (e.g. estimation error) and demonstrate the usefulness of credit risk modelling through case studies. This book provides practitioners and students with an intuitive, hands-on introduction to modern credit risk modelling. Every chapter starts with an explanation of the methodology and then the authors take the reader step by step through the implementation of the methods in Excel and VBA. They focus specifically on risk management issues and cover default probability estimation (scoring, structural models, and transition matrices), correlation and portfolio analysis, validation, as well as credit default swaps and structured finance. The book has an accompanying website, https://creditriskmodeling.wordpress.com/, which has been specially updated for this Second Edition and contains slides and exercises for lecturers.

Economic Models, Estimation and Risk Programming: Essays in Honor of Gerhard Tintner

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Author :
Publisher : Springer Science & Business Media
ISBN 13 : 3642461980
Total Pages : 474 pages
Book Rating : 4.6/5 (424 download)

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Book Synopsis Economic Models, Estimation and Risk Programming: Essays in Honor of Gerhard Tintner by : K. A. Fox

Download or read book Economic Models, Estimation and Risk Programming: Essays in Honor of Gerhard Tintner written by K. A. Fox and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: These essays in honor of Professor Gerhard Tintner are substantive contributions to three areas of econometrics, (1) economic models and applications,. (2) estimation, and (3) stochastic programming, in each of which he has labored with outstanding success. His own work has extended into multivariate analysis, the pure theory of decision-making under un certainty, and other fields which are not touched upon here for reasons of space and focus. Thus, this collection is appropriate to his interests but covers much less than their full range. Professor Tintner's contributions to econometrics through teaching, writing, editing, lecturing and consulting have been varied and inter national. We have tried to highlight them in "The Econometric Work of Gerhard Tintner" and to place them in historical perspective in "The Invisible Revolution in Economics: Emergence of a Mathematical Science. " Professor Tintner's career to date has spanned the organizational life of the Econometric Society and his contributions have been nearly coextensive with its scope. His principal books and articles up to 1968 are listed in the "Selected Bibliography. " Professor Tintner's current research involves the intricate problems of specification and application of stochastic processes to economic systems, particularly to growth, diffusion of technology, and optimal control. As always, he is moving with the econometric frontier and a portion of the frontier is moving with him. IV Two of the editors wrote dissertations under Professor Tintner's sup- vision; the third knew him as a colleague and friend.