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**Carol Alexander – Market Risk Analysis Vol. IV. Value-At-Risk Models**

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.
- Table of Contents
- List of Figures.
- List of Tables.
- List of Examples.
- Preface to Volume IV.
- 1 Value at Risk and Other Risk Metrics.
- 1.1 Introduction.
- 1.2 An Overview of Market Risk Assessment.
- 1.3 Downside and Quantile Risk Metrics.
- 1.4 Defining Value at Risk.
- 1.5 Foundations of Value-at-Risk Measurement.
- 1.6 Risk Factor Value at Risk.
- 1.7 Decomposition of Value at Risk.
- 1.8 Risk Metrics Associated with Value at Risk.
- 1.9 Introduction to Value-at-Risk Models.
- 1.10 Summary and Conclusions.
- 2 Parametric Linear VaR Models.
- 2.1 Introduction.
- 2.2 Foundations of Normal Linear Value at Risk.
- 2.3 Normal Linear Value at Risk for Cash-Flow Maps.
- 2.4 Case Study: PC Value at Risk of a UK Fixed Income Portfolio.
- 2.5 Normal Linear Value at Risk for Stock Portfolios.
- 2.6 Systematic Value-at-Risk Decomposition for Stock Portfolios.
- 2.7 Case Study: Normal Linear Value at Risk for Commodity Futures.
- 2.8 Student
*t*Distributed Linear Value at Risk. - 2.9 Linear Value at Risk with Mixture Distributions.
- 2.10 Exponential Weighting with Parametric Linear Value at Risk.
- 2.11 Expected Tail Loss (Conditional VaR).
- 2.12 Case Study: Credit Spread Parametric Linear Value at Risk and ETL.
- 2.13 Summary and Conclusions.
- 3 Historical Simulation.
- 3.1 Introduction.
- 3.2 Properties of Historical Value at Risk.
- 3.3 Improving the Accuracy of Historical Value at Risk.
- 3.4 Precision of Historical Value at Risk at Extreme Quantiles.
- 3.5 Historical Value at Risk for Linear Portfolios.
- 3.6 Estimating Expected Tail Loss in the Historical Value-at-Risk Model.
- 3.7 Summary and Conclusions.
- 4 Monte Carlo VaR.
- 4.1 Introduction.
- 4.2 Basic Concepts.
- 4.3 Modelling Dynamic Properties in Risk Factor Returns.
- 4.4 Modelling Risk Factor Dependence.
- 4.5 Monte Carlo Value at Risk for Linear Portfolios.
- 4.6 Summary and Conclusions.
- 5 Value at Risk for Option Portfolios.
- 5.1 Introduction.
- 5.2 Risk Characteristics of Option Portfolios.
- 5.3 Analytic Value-at-Risk Approximations.
- 5.4 Historical Value at Risk for Option Portfolios.
- 5.5 Monte Carlo Value at Risk for Option Portfolios.
- 5.6 Summary and Conclusions.
- 6 Risk Model Risk.
- 6.1 Introduction.
- 6.2 Sources of Risk Model Risk.
- 6.3 Estimation Risk.

IV.6.4 Model Validation.

IV.6.5 Summary and Conclusions.

IV.7 Scenario Analysis and Stress Testing.

IV.7.1 Introduction.

IV.7.2 Scenarios on Financial Risk Factors.

IV.7.3 Scenario Value at Risk and Expected Tail Loss.

IV.7.4 Introduction to Stress Testing.

IV.7.5 A Coherent Framework for Stress Testing.

IV.7.6 Summary and Conclusions.

IV.8 Capital Allocation.

IV.8.1 Introduction.

IV.8.2 Minimum Market Risk Capital Requirements for Banks.

IV.8.3 Economic Capital Allocation.

IV.8.4 Summary and Conclusions.

References.

Author Information

Carol Alexander is a Professor of Risk Management at the ICMA Centre, University of Reading, and Chair of the Academic Advisory Council of the Professional Risk Manager’s International Association (PRMIA). She is the author of *Market Models: A Guide to Financial Data Analysis*(John Wiley & Sons Ltd, 2001) and has been editor and contributor of a very large number of books in finance and mathematics, including the multi-volume *Professional Risk Manager’s Handbook *(McGraw-Hill, 2008 and PRMIA Publications). Carol has published nearly 100 academic journal articles, book chapters and books, the majority of which focus on financial risk management and mathematical finance. Professor Alexander is one of the world’s leading authorities on market risk analysis.

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