During the last decade, problems in the world of finance have been the main driving force for developing sophisticated mathematical methods which may be used for identifying and measuring risk. The focus is still on quantifying market and credit risk, but general operational risks will become more important in the future. In this book the reader will find approaches from economic theory, allocation problems, credit scoring, volatility structures, general market risk, country risk and extreme value theory. The contributions of this book reflect the views of leading practitioners and academics in the field of risk management. Most of the models considered for the evolution of asset values are of a complex and stochastic nature, including stochastic volatility models in continuous time as well as their counterparts in discrete time, the family of GARCH-like time series. The contents reflect the fact that a major part of recent research has been motivated by applications in finance, but most of the mathematical approaches may be used for risk analysis in engineering and science in a rather straightforward manner. As known from insurance mathematics for some time, extreme damages from natural disaster follow similar stochastic laws as extreme losses from certain investments. The articles discuss critical concepts such as value-at-risk, volatility and other risk masures in nonstandard situations. Stochastic processes beyond geometric Brownian motion allow for a more realistic reflection of stylized facts like leptokurtosis or skewness of return distrubutions which often are observed in real data. Procedures for detecting change points in time series allow for dealing with the risk of a sudden structural change of the market. Models for extremal events in financial time series or stochastic processes in continuous time are of prime importance for risk management as, in practice, these rare events frequently dominate the whole profit/loss-process. Complex dynamic processes of life and sciences generate risks that have to be taken. The need for clear and distinctive definitions of different kinds of risks, adequate methods and parsimonious models is obvious. The identification of important risk factors and the quantification of risk stemming from an interplay between many risk factors is a prerequisite for mastering the challenges of risk perception, analysis and management successfully. The increasing complexity of stochastic systems, especially in finance, have catalysed the use of advanced statistical methods for these tasks. The methodological approach to solving risk management tasks may, however, be undertaken from many different angles. A financial insti tution may focus on the risk created by the use of options and other derivatives in global financial processing, an auditor will try to evalu ate internal risk management models in detail, a mathematician may be interested in analysing the involved nonlinearities or concentrate on extreme and rare events of a complex stochastic system, whereas a statis tician may be interested in model and variable selection, practical im plementations and parsimonious modelling. An economist may think about the possible impact of risk management tools in the framework of efficient regulation of financial markets or efficient allocation of capital. Front Matter....Pages i-xiii Allocation of Economic Capital in loan portfolios....Pages 1-17 Estimating Volatility for Long Holding Periods....Pages 19-31 A Simple Approach to Country Risk....Pages 33-67 Predicting Bank Failures in Transition: Lessons from the Czech Bank Crisis of the mid-Nineties....Pages 69-81 Credit Scoring using Semiparametric Methods....Pages 83-97 On the (Ir)Relevancy of Value-at-Risk Regulation....Pages 99-117 Backtesting beyond VaR....Pages 119-130 Measuring Implied Volatility Surface Risk using Principal Components Analysis....Pages 131-148 Detection and estimation of changes in ARCH processes....Pages 149-160 Behaviour of Some Rank Statistics for Detecting Changes....Pages 161-174 A stable CAPM in the presence of heavy-tailed distributions....Pages 175-188 A Tailored Suit for Risk Management: Hyperbolic Model....Pages 189-202 Computational Resources for Extremes....Pages 203-213 Confidence intervals for a tail index estimator....Pages 215-222 Extremes of alpha-ARCH Models....Pages 223-257 Back Matter....Pages 259-260
This collection of articles by leading researchers will be of interest to people working in the area of mathematical finance.
