Market Risk Analysis, Value at Risk Models

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. For further details, see www.carolalexander.org

• List of Figures xiiiList of Tables xviList of Examples xxiForeword xxvPreface to Volume IV xxixIV.1 Value at Risk and Other Risk Metrics 1IV.1.1 Introduction 1IV.1.2 An Overview of Market Risk Assessment 4IV.1.3 Downside and Quantile Risk Metrics 9IV.1.4 Defining Value at Risk 13IV.1.5 Foundations of Value-at-Risk Measurement 17IV.1.6 Risk Factor Value at Risk 25IV.1.7 Decomposition of Value at Risk 30IV.1.8 Risk Metrics Associated with Value at Risk 33IV.1.9 Introduction to Value-at-Risk Models 41IV.1.10 Summary and Conclusions 47IV.2 Parametric Linear VaR Models 53IV.2.1 Introduction 53IV.2.2 Foundations of Normal Linear Value at Risk 56IV.2.3 Normal Linear Value at Risk for Cash-Flow Maps 67IV.2.4 Case Study: PC Value at Risk of a UK Fixed Income Portfolio 79IV.2.5 Normal Linear Value at Risk for Stock Portfolios 85IV.2.6 Systematic Value-at-Risk Decomposition for Stock Portfolios 93IV.2.7 Case Study: Normal Linear Value at Risk for Commodity Futures 103IV.2.8 Student t Distributed Linear Value at Risk 106IV.2.9 Linear Value at Risk with Mixture Distributions 111IV.2.10 Exponential Weighting with Parametric Linear Value at Risk 121IV.2.11 Expected Tail Loss (Conditional VaR) 128IV.2.12 Case Study: Credit Spread Parametric Linear Value at Risk and ETL 135IV.2.13 Summary and Conclusions 138IV.3 Historical Simulation 141IV.3.1 Introduction 141IV.3.2 Properties of Historical Value at Risk 144IV.3.3 Improving the Accuracy of Historical Value at Risk 152IV.3.4 Precision of Historical Value at Risk at Extreme Quantiles 165IV.3.5 Historical Value at Risk for Linear Portfolios 175IV.3.6 Estimating Expected Tail Loss in the Historical Value-at-Risk Model 195IV.3.7 Summary and Conclusions 198IV.4 Monte Carlo VaR 201IV.4.1 Introduction 201IV.4.2 Basic Concepts 203IV.4.3 Modelling Dynamic Properties in Risk Factor Returns 215IV.4.4 Modelling Risk Factor Dependence 225IV.4.5 Monte Carlo Value at Risk for Linear Portfolios 233IV.4.6 Summary and Conclusions 244IV.5 Value at Risk for Option Portfolios 247IV.5.1 Introduction 247IV.5.2 Risk Characteristics of Option Portfolios 250IV.5.3 Analytic Value-at-Risk Approximations 257IV.5.4 Historical Value at Risk for Option Portfolios 262IV.5.5 Monte Carlo Value at Risk for Option Portfolios 282IV.5.6 Summary and Conclusions 307IV.6 Risk Model Risk 311IV.6.1 Introduction 311IV.6.2 Sources of Risk Model Risk 313IV.6.3 Estimation Risk 324IV.6.4 Model Validation 332IV.6.5 Summary and Conclusions 353IV.7 Scenario Analysis and Stress Testing 357IV.7.1 Introduction 357IV.7.2 Scenarios on Financial Risk Factors 359IV.7.3 Scenario Value at Risk and Expected Tail Loss 367IV.7.4 Introduction to Stress Testing 378IV.7.5 A Coherent Framework for Stress Testing 384IV.7.6 Summary and Conclusions 398IV.8 Capital Allocation 401IV.8.1 Introduction 401IV.8.2 Minimum Market Risk Capital Requirements for Banks 403IV.8.3 Economic Capital Allocation 416IV.8.4 Summary and Conclusions 433References 437Index 441