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In the recent literature, methods from extreme value theory (EVT) have frequently been applied for the estimation of tail risk measures. While previous analyses show that EVT methods often lead to accurate estimates for risk measures, a potential drawback lies in high standard errors of point estimates of these methods as only a fraction of the data set is used. Thus, the aim of this paper is to comprehensively study the impact of model risk on EVT methods when determining the Value-at-Risk and Expected Shortfall. We distinguish between misspecification, estimation and prediction risk and show that methods from extreme value theory are less prone to misspecification and estimation risk, however, they exhibit a higher sensitivity towards prediction risk. We find that this can lead to more severe Value-at-Risk and Expected Shortfall underestimations than for traditional estimation methods in extreme cases. Hence, we show how sources of model risk should be taken into account for the quantification of capital requirements, in order to provide sufficient capital levels in the presence of model risk.
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
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.
While operational risk has long been regarded as a mere part of "other" risks--outside the realm of credit and market risk--it has quickly made its way to the forefront of finance. In fact, with implementation of the Basel II Capital Accord already underway, many financial professionals--as well as those preparing to enter this field--must now become familiar with a variety of issues related to operational risk modeling and management. Written by the experienced team of Anna Chernobai, Svetlozar Rachev, and Frank Fabozzi, Operational Risk will introduce you to the key concepts associated with this discipline. Filled with in-depth insights, expert advice, and innovative research, this comprehensive guide not only presents you with an abundant amount of information regarding operational risk, but it also walks you through a wide array of examples that will solidify your understanding of the issues discussed. Topics covered include: The main challenges that exist in modeling operational risk. The variety of approaches used to model operational losses. Value-at-Risk and its role in quantifying and managing operational risk. The three pillars of the Basel II Capital Accord. And much more.
It appears that we live in an age of disasters: the mighty Missis sippi and Missouri flood millions of acres, earthquakes hit Tokyo and California, airplanes crash due to mechanical failure and the seemingly ever increasing wind speeds make the storms more and more frightening. While all these may seem to be unexpected phenomena to the man on the street, they are actually happening according to well defined rules of science known as extreme value theory. We know that records must be broken in the future, so if a flood design is based on the worst case of the past then we are not really prepared against floods. Materials will fail due to fatigue, so if the body of an aircraft looks fine to the naked eye, it might still suddenly fail if the aircraft has been in operation over an extended period of time. Our theory has by now penetrated the so cial sciences, the medical profession, economics and even astronomy. We believe that our field has come of age. In or~er to fully utilize the great progress in the theory of extremes and its ever increasing acceptance in practice, an international conference was organized in which equal weight was given to theory and practice. This book is Volume I of the Proceedings of this conference. In selecting the papers for Volume lour guide was to have authoritative works with a large variety of coverage of both theory and practice.
Operational Risk While operational risk has long been regarded as a mere part of "other" risks—outside the realm of credit and market risk—it has quickly made its way to the forefront of finance. In fact, with implementation of the Basel II Capital Accord already underway, many financial professionals—as well as those preparing to enter this field—must now become familiar with a variety of issues related to operational risk modeling and management. Written by the experienced team of Anna Chernobai, Svetlozar Rachev, and Frank Fabozzi, Operational Risk: A Guide to Basel II Capital Requirements, Models, and Analysis will introduce you to the key concepts associated with this discipline. Filled with in-depth insights, expert advice, and innovative research, this comprehensive guide not only presents you with an abundant amount of information regarding operational risk, but it also walks you through a wide array of examples that will solidify your understanding of the issues discussed. Topics covered include: The main challenges that exist in modeling operational risk The variety of approaches used to model operational losses Value-at-Risk and its role in quantifying and managing operational risk The three pillars of the Basel II Capital Accord And much more
In this paper we point out several pitfalls of the standard methodologies for quantifying operational losses. Firstly, we use Extreme Value Theory to model real heavy-tailed data. We show that using the Value-at-Risk as a risk measure may lead to a mis-estimation of the capital requirements. In particular, we examine the issues of stability and coherence and relate them to the degree of heavy-tailedness of the data. Secondly, we introduce dependence between the business lines using Copula Theory. We show that standard economic thinking about diversification may be inappropriate when infinite-mean distributions are involved.
A practical, accessible step-by-step analysis of the theory and practicalities of credit risk measurement and management.
Seminar paper from the year 2004 in the subject Business economics - Controlling, grade: 1,7, European Business School - International University Schloß Reichartshausen Oestrich-Winkel (Department of Accounting and Control), language: English, abstract: The risk and return framework is generally accepted and discussed by scientists, at least since Markowitz introduced his Portfolio Theory in 1952. Subsequently, models were developed to evaluate investments under consideration of risk and return. Traditionally, practitioners primarily focused on past earnings as a measure of the profitability of an investment, without adequately considering potential risks. Therefore, the development of professional risk management systems was often neglected. Thus, the possibility of high losses was not appropriately incorporated in their investment strategies. The consequences of such mistreatment became evident in the mid 1990s, when some of the world’s largest companies faced huge losses and sometimes even insolvency. Most of these failures were a direct result of inappropriate use of financial instruments and insufficient internal control mechanisms. The most spectacular debacles even resulted in losses of more than one billion dollars for each affected institution. In case of Barings Bank, a single trader ruined the 233-year old British financial institution by inappropriate investments in high-risk futures in 1995. The consequent loss of $1.3 billion, realized in a very short period, could not be absorbed and forced the downfall of Barings. At Daiwa Bank, it was also a single trader who caused a $1.1 billion deficit. In contrast, the losses were accumulated over 11 years from 1984. Another well-publicized bankruptcy was declared in 1994 by the Californian Orange County, after losses of $1.8 billion. Such evidence of poor risk management and control shows that proper financial risk management is crucial for all kinds of institutions in order to guarantee stability and continuity. Therefore, it is necessary to establish adequate risk management processes and to develop appropriate tools, which quantify risk exposures of both entire institutions and single financial instruments. This risk quantification should alert management early enough to prevent exceptional losses. One of the key concepts addressing these prob-lems of modern risk management was introduced in 1993 with the Value-at-Risk (VaR) models.