Details

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

<p>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 <i>Market Models: A Guide to Financial Data Analysis</i> (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 <i>Professional Risk Manager’s Handbook</i> (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. <p>Professor Alexander is one of the world’s leading authorities on market risk analysis. For further details, see <b>www.carolalexander.org</b>

<p>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. <p>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 <i>interactive Excel spreadsheets</i> available from the accompanying website. Excel examples and case studies provided with this volume include: <ul><li>Parametric linear value at risk (VaR) models: normal, Student <i>t</i> and normal mixture and their expected tail loss (ETL);</li> <li>New formulae for VaR based on autocorrelated returns;</li> <li>Historical simulation VaR models: how to scale historical VaR and volatility adjusted historical VaR;</li> <li>Monte Carlo simulation VaR models based on multivariate normal and Student <i>t</i> distributions, and based on copulas;</li> <li>Examples and case studies of numerous applications to interest rate sensitive, equity, commodity and international portfolios;</li> <li>Decomposition of systematic VaR of large portfolios into stand-alone and marginal VaR components;</li> <li>Backtesting and the assessment of risk model risk;</li> <li>Hypothetical and historical stress tests, liquidity adjustment to VaR, and stress testing based on VaR and ETL.</li></ul>

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