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Modelling Operational Risk Using A Bayesian Approach To Extreme Value Theory


Modelling Operational Risk Using A Bayesian Approach To Extreme Value Theory
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Modelling Operational Risk Using A Bayesian Approach To Extreme Value Theory


Modelling Operational Risk Using A Bayesian Approach To Extreme Value Theory
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Author : María Elena Rivera Mancía
language : en
Publisher:
Release Date : 2014

Modelling Operational Risk Using A Bayesian Approach To Extreme Value Theory written by María Elena Rivera Mancía and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with categories.


"Extreme-value theory is concerned with the tail behaviour of probability distributions. In recent years, it has found many applications in areas as diverse as hydrology, actuarial science, and finance, where complex phenomena must often be modelled from a small number of observations.Extreme-value theory can be used to assess the risk of rare events either through the block maxima or peaks-over-threshold method. The choice of threshold is both influential and delicate, as a balance between the bias and variance of the estimates is required. At present, this threshold is often chosen arbitrarily, either graphically or by setting it as some high quantile of the data.Bayesian inference is an alternative to deal with this problem by treating the threshold as a parameter in the model. In addition, a Bayesian approach allows for the incorporation of internal and external observations in combination with expert opinion, thereby providing a natural probabilistic framework to evaluate risk models.This thesis presents a Bayesian inference framework for extremes. We focus on a model proposed by Behrens et al. (2004), where an analysis of extremes is performed using a mixture model that combines a parametric form for the centre and a Generalized Pareto Distribution (GPD) for the tail of the distribution. Our approach accounts for all the information available in making inference about the unknown parameters from both distributions, the threshold included. A Bayesian analysis is then performed by using expert opinions to determine the parameters for prior distributions; posterior inference is carried out through Markov Chain Monte Carlo methods. We apply this methodology to operational risk data to analyze its performance.The contributions of this thesis can be outlined as follows:-Bayesian models have been barely explored in operational risk analysis. In Chapter 3, we show how these models can be adapted to operational risk analysis using fraud data collected by different banks between 2007 and 2010. By combining prior information to the data, we can estimate the minimum capital requirement and risk measures such as the Value-at-Risk (VaR) and the Expected Shortfall (ES) for each bank.-The use of expert opinion plays a fundamental role in operational risk modelling. However, most of time this issue is not addressed properly. In Chapter 4, we consider the context of the problem and show how to construct a prior distribution based on measures that experts are familiar with, including VaR and ES. The purpose is to facilitate prior elicitation and reproduce expert judgement faithfully.-In Section 4.3, we describe techniques for the combination of expert opinions. While this issue has been addressed in other fields, it is relatively recent in our context. We examine how different expert opinions may influence the posterior distribution and how to build a prior distribution in this case. Results are presented on simulated and real data.-In Chapter 5, we propose several new mixture models with Gamma and Generalized Pareto elements. Our models improve upon previous work by Behrens et al. (2004) since the loss distribution is either continuous at a fixed quantile or it has continuous first derivative at the blend point. We also consider the cases when the scaling is arbitrary and when the density is discontinuous.-Finally, we introduce two nonparametric models. The first one is based on the fact that the GPD model can be represented as a Gamma mixture of exponential distributions, while the second uses a Dirichlet process prior on the parameters of the GPD model." --



Multivariate Estimation For Operational Risk With Judicious Use Of Extreme Value Theory


Multivariate Estimation For Operational Risk With Judicious Use Of Extreme Value Theory
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Author : Mahmoud El-Gamal
language : en
Publisher: CreateSpace
Release Date : 2014-12-31

Multivariate Estimation For Operational Risk With Judicious Use Of Extreme Value Theory written by Mahmoud El-Gamal and has been published by CreateSpace this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-31 with categories.


The Basel II Accord requires participating banks to quantify operational risk according to a matrix of business lines and event types. Proper modeling of univariate loss distributions and dependence structures across those categories of operational losses is critical for proper assessment of overall annual operational loss distributions. We illustrate our proposed methodology using Loss Data Collection Exercise 2004 (LDCE 2004) data on operational losses across five loss event types. We estimate a multivariate likelihood-based statistical model, which illustrates the benefits and risks of using extreme value theory (EVT) in modeling univariate tails of event type loss distributions. We find that abandoning EVT leads to unacceptably low estimates of risk capital requirements, while indiscriminate use of EVT to all data leads to unacceptably high ones. The judicious middle approach is to use EVT where dictated by data, and after separating clear outliers that need to be modeled via probabilistic scenario analysis. We illustrate all computational steps in estimation of marginal distributions and copula with an application to one bank's data (disguising magnitudes to ensure that bank's anonymity). The methods we use to overcome heretofore unexplored technical problems in estimation of codependence across risk types scales easily to larger models, encompassing not only operational, but also other types of risks.



Modelling Operational Risk Using Bayesian Inference


Modelling Operational Risk Using Bayesian Inference
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Author : Pavel V. Shevchenko
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-01-19

Modelling Operational Risk Using Bayesian Inference written by Pavel V. Shevchenko and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-19 with Business & Economics categories.


The management of operational risk in the banking industry has undergone explosive changes over the last decade due to substantial changes in the operational environment. Globalization, deregulation, the use of complex financial products, and changes in information technology have resulted in exposure to new risks which are very different from market and credit risks. In response, the Basel Committee on Banking Supervision has developed a new regulatory framework for capital measurement and standards for the banking sector. This has formally defined operational risk and introduced corresponding capital requirements. Many banks are undertaking quantitative modelling of operational risk using the Loss Distribution Approach (LDA) based on statistical quantification of the frequency and severity of operational risk losses. There are a number of unresolved methodological challenges in the LDA implementation. Overall, the area of quantitative operational risk is very new and different methods are under hot debate. This book is devoted to quantitative issues in LDA. In particular, the use of Bayesian inference is the main focus. Though it is very new in this area, the Bayesian approach is well suited for modelling operational risk, as it allows for a consistent and convenient statistical framework for quantifying the uncertainties involved. It also allows for the combination of expert opinion with historical internal and external data in estimation procedures. These are critical, especially for low-frequency/high-impact operational risks. This book is aimed at practitioners in risk management, academic researchers in financial mathematics, banking industry regulators and advanced graduate students in the area. It is a must-read for anyone who works, teaches or does research in the area of financial risk.



Advances In Heavy Tailed Risk Modeling


Advances In Heavy Tailed Risk Modeling
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Author : Gareth W. Peters
language : en
Publisher: John Wiley & Sons
Release Date : 2015-05-21

Advances In Heavy Tailed Risk Modeling written by Gareth W. Peters and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-21 with Mathematics categories.


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.



Scenario Analysis In Risk Management


Scenario Analysis In Risk Management
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Author : Bertrand K. Hassani
language : en
Publisher: Springer
Release Date : 2016-10-26

Scenario Analysis In Risk Management written by Bertrand K. Hassani and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-26 with Business & Economics categories.


This book focuses on identifying and explaining the key determinants of scenario analysis in the context of operational risk, stress testing and systemic risk, as well as management and planning. Each chapter presents alternative solutions to perform reliable scenario analysis. The author also provides technical notes and describes applications and key characteristics for each of the solutions. In addition, the book includes a section to help practitioners interpret the results and adjust them to real-life management activities. Methodologies, including those derived from consensus strategies, extreme value theory, Bayesian networks, Neural networks, Fault Trees, frequentist statistics and data mining are introduced in such a way as to make them understandable to readers without a quantitative background. Particular emphasis is given to the added value of the implementation of these methodologies.



Extreme Value Modeling And Risk Analysis


Extreme Value Modeling And Risk Analysis
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Author : Dipak K. Dey
language : en
Publisher: CRC Press
Release Date : 2016-01-06

Extreme Value Modeling And Risk Analysis written by Dipak K. Dey and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-06 with Mathematics categories.


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



Operational Risk Assessment


Operational Risk Assessment
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Author : Brendon Young
language : en
Publisher: John Wiley & Sons
Release Date : 2010-12-03

Operational Risk Assessment written by Brendon Young and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-12-03 with Business & Economics categories.


Operational risk assessment The Commercial Imperative of a More Forensic and Transparent Approach Brendon Young and Rodney Coleman “Brendon Young and Rodney Coleman's book is extremely timely. There has never been a greater need for the financial industry to reassess the way it looks at risk. [...] They are right to draw attention to the current widespread practices of risk management, which [...] have allowed risk to become underpriced across the entire industry.” Rt Hon John McFall MP, Chairman, House of Commons Treasury Committee Failure of the financial services sector to properly understand risk was clearly demonstrated by the recent 'credit crunch'. In its 2008 Global Stability Report, the IMF sharply criticised banks and other financial institutions for the failure of risk management systems, resulting in excessive risk-taking. Financial sector supervision and regulation was also criticised for lagging behind shifts in business models and rapid innovation. This book provides investors with a sound understanding of the approaches used to assess the standing of firms and determine their true potential (identifying probable losers and potential longer-term winners). It advocates a 'more forensic' approach towards operational risk management and promotes transparency, which is seen as a facilitator of competition and efficiency as well as being a barrier to fraud, corruption and financial crime. Risk assessment is an integral part of informed decision making, influencing strategic positioning and direction. It is fundamental to a company’s performance and a key differentiator between competing management teams. Increasing complexity is resulting in the need for more dynamic, responsive approaches to the assessment and management of risk. Not all risks can be quantified; however, it remains incumbent upon management to determine the impact of possible risk-events on financial statements and to indicate the level of variation in projected figures. To begin, the book looks at traditional methods of risk assessment and shows how these have developed into the approaches currently being used. It then goes on to consider the more advanced forensic techniques being developed, which will undoubtedly increase understanding. The authors identify 'best practice' and address issues such as the importance of corporate governance, culture and ethics. Insurance as a mitigant for operational risk is also considered. Quantitative and qualitative risk assessment methodologies covered include: Loss-data analysis; extreme value theory; causal analysis including Bayesian Belief Networks; control risk self-assessment and key indicators; scenario analysis; and dynamic financial analysis. Views of industry insiders, from organisations such as Standard & Poors, Fitch, Hermes, USS, UN-PRI, Deutsche Bank, and Alchemy Partners, are presented together with those from experts at the FSA, the International Accounting Standards Board (IASB), and the Financial Reporting Council. In addition to investors, this book will be of interest to actuaries, rating agencies, regulators and legislators, as well as to the directors and risk managers of financial institutions in both the private and public sectors. Students requiring a comprehensive knowledge of operational risk management will also find the book of considerable value.



Operational Risk


Operational Risk
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Author : Harry H. Panjer
language : en
Publisher: John Wiley & Sons
Release Date : 2006-10-13

Operational Risk written by Harry H. Panjer and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-10-13 with Business & Economics categories.


Discover how to optimize business strategies from both qualitative and quantitative points of view Operational Risk: Modeling Analytics is organized around the principle that the analysis of operational risk consists, in part, of the collection of data and the building of mathematical models to describe risk. This book is designed to provide risk analysts with a framework of the mathematical models and methods used in the measurement and modeling of operational risk in both the banking and insurance sectors. Beginning with a foundation for operational risk modeling and a focus on the modeling process, the book flows logically to discussion of probabilistic tools for operational risk modeling and statistical methods for calibrating models of operational risk. Exercises are included in chapters involving numerical computations for students' practice and reinforcement of concepts. Written by Harry Panjer, one of the foremost authorities in the world on risk modeling and its effects in business management, this is the first comprehensive book dedicated to the quantitative assessment of operational risk using the tools of probability, statistics, and actuarial science. In addition to providing great detail of the many probabilistic and statistical methods used in operational risk, this book features: * Ample exercises to further elucidate the concepts in the text * Definitive coverage of distribution functions and related concepts * Models for the size of losses * Models for frequency of loss * Aggregate loss modeling * Extreme value modeling * Dependency modeling using copulas * Statistical methods in model selection and calibration Assuming no previous expertise in either operational risk terminology or in mathematical statistics, the text is designed for beginning graduate-level courses on risk and operational management or enterprise risk management. This book is also useful as a reference for practitioners in both enterprise risk management and risk and operational management.



Modeling Measuring And Hedging Operational Risk


Modeling Measuring And Hedging Operational Risk
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Author : Marcelo G. Cruz
language : en
Publisher: John Wiley & Sons
Release Date : 2002-03-12

Modeling Measuring And Hedging Operational Risk written by Marcelo G. Cruz and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-03-12 with Business & Economics categories.


Worldwide banks are keen to find ways of effectively measuring and managing operational risk , yet many find themselves poorly equipped to do this. Operational risk includes concerns about such issues as transaction processing errors, liability situations, and back-office failure. Measuring and Modelling Operational Risk focuses on the measuring and modelling techniques banks and investment companies need to quantify operational risk and provides practical, sensible solutions for doing so. * Author is one of the leading experts in the field of operational risk. * Interest in the field is growing rapidly and this is the only book that focuses on the quantitative measuring and modelling of operational risk. * Includes case vignettes and real-world examples based on the author's extensive experience.



Operational Risk Modeling In Financial Services


Operational Risk Modeling In Financial Services
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Author : Patrick Naim
language : en
Publisher: John Wiley & Sons
Release Date : 2019-05-28

Operational Risk Modeling In Financial Services written by Patrick Naim and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-28 with Business & Economics categories.


Transform your approach to oprisk modelling with a proven, non-statistical methodology Operational Risk Modeling in Financial Services provides risk professionals with a forward-looking approach to risk modelling, based on structured management judgement over obsolete statistical methods. Proven over a decade’s use in significant banks and financial services firms in Europe and the US, the Exposure, Occurrence, Impact (XOI) method of operational risk modelling played an instrumental role in reshaping their oprisk modelling approaches; in this book, the expert team that developed this methodology offers practical, in-depth guidance on XOI use and applications for a variety of major risks. The Basel Committee has dismissed statistical approaches to risk modelling, leaving regulators and practitioners searching for the next generation of oprisk quantification. The XOI method is ideally suited to fulfil this need, as a calculated, coordinated, consistent approach designed to bridge the gap between risk quantification and risk management. This book details the XOI framework and provides essential guidance for practitioners looking to change the oprisk modelling paradigm. Survey the range of current practices in operational risk analysis and modelling Track recent regulatory trends including capital modelling, stress testing and more Understand the XOI oprisk modelling method, and transition away from statistical approaches Apply XOI to major operational risks, such as disasters, fraud, conduct, legal and cyber risk The financial services industry is in dire need of a new standard — a proven, transformational approach to operational risk that eliminates or mitigates the common issues with traditional approaches. Operational Risk Modeling in Financial Services provides practical, real-world guidance toward a more reliable methodology, shifting the conversation toward the future with a new kind of oprisk modelling.