Cover -- Half-title -- Title -- Copyright -- CONTENTS -- Contributors -- Introduction -- Quantifying the Risks of Trading -- Abstract -- 1 Introduction -- 2 Market valuation and valuation uncertainty -- 2.1 Discounted cash flow formula -- 2.2 Types of revaluation models -- 2.3 Revaluation systems and valuation error -- 2.4 Sources of valuation differences and valuation error -- 3 Market errors -- 3.1 General and specific market risk factors -- 4 Introduction to market risk measurement -- 4.1 Types of market risk -- 4.2 Types of market risk measurement -- 4.3 Scenario measurements of market risk -- 4.4 Statistical measurements of market risk -- 4.5 Holding period and assumption of static portfolio -- 4.6 Limitations on VAR -- 4.7 The two basic components of VAR calculation -- 5 VAR: Simulating changes in market factors -- 5.1 Historical simulation -- 5.2 Parametric statistical simulation -- 5.3 Technical issues in simulating changes in market factors -- 5.4 Covariance matrix -- 5.5 Positive definiteness -- 5.6 Completeness of market factors -- 5.7 Simulation of market risk with specific risk -- 6 VAR: simulating changes in portfolio value -- 6.1 Full valuation -- 6.2 Parametric portfolio revaluation -- 6.3 Grids of factor sensitivities and the terms of a Tay-lor series expansion -- 6.4 Parametric portfolio revaluation and the represen-tation of yield curve -- 7 Pre-settlement counterparty credit exposure -- 7.1 Forms of credit risk -- 7.2 Defining pre-settlement exposure -- 7.3 Credit exposure and credit risk -- 7.4 Contrasting the exposure of Lending Risk, Issuer Risk and Pre-Settlement Risk -- 7.5 Pre-settlement exposure to options -- 7.6 Pre-settlement exposure of multiple contracts and netting -- 7.7 Pre-settlement exposure and potential future re-placement cost -- 7.8 Simple transaction exposure method of measuring pre-settlement exposure.

7.9 BIS requirements for pre-settlement credit risk -- 7.10 Limitations of simple transaction method -- 7.11 Counterparty portfolio simulation method and counterparty exposure profile -- 7.12 Effects of a margin agreement on exposure and risk -- 7.13 Economic capital for pre-settlement risk-general principles -- 7.14 Economic capital for pre-settlement risk-simple example -- 8 Comparing and contrasting market risk and pre-settlement risk -- Value at Risk Analysis of a Leveraged Swap -- Abstract -- 1 Introduction -- 2 The Details of the Contract -- The Original Contract -- Modifications of the Contract -- The Swap and the Embedded Option -- The Analysis Date and Data -- The Value of the Contract -- 3 The Nature of the Bet -- The Ex Post Behavior of Interest Rates and the Spread -- 4 Value at Risk -- The Horizon -- The Model Implementation -- Notes on the Implementation and Choice of Model -- The Initial Term Structure and Forward Curve -- The Volatility Estimation -- The Option Delta -- Sample Term Structures after 6 Months -- The Spread and Future Contract Values -- 5 Conclusion -- Acknowledgments -- References -- Stress Testing in a Value at Risk Framework -- Abstract -- Introduction -- 1 A Review of the VaR Framework -- 2 Stress Testing in the Context of VaR -- 3 Stress Tests Scenarios based upon Historical Covariances -- 4 Accuracy of Stress Tests that use Historical Distributions -- Data -- Identifying Stress Events -- Stress Test Scenarios -- Results -- Anomalies -- 5 Stress Testing with Volatility and Correlation Shocks -- Stressing Volatilities -- Shocking Volatilities and Correlations -- 6 Issues Regarding Full Repricing -- 7 Practical Issues Related to Scenario Specification -- 8 Concluding Remarks -- References -- Dynamic Portfolio Replication Using Stochastic Programming -- Abstract -- 1 Introduction.

2 The dynamic stochastic programming approach -- 3 Constructing dynamic replicating strategies using DSP -- Tracking problems -- Scenario trees -- The optimization problem -- The transaction cost model -- Turning the solution into a trading strategy -- 4 The options problem -- The target -- The tradable instruments -- The scenario tree -- 5 Numerical Experiments -- Portfolio compression -- Dynamic portfolio replication -- Benchmark results -- Experiments varying tree size -- Experiments varying initial branching -- 6 Conclusions -- Acknowledgements -- References -- Credit and Interest Rate Risk -- Abstract -- 1 Introduction -- 1.1 VaRs for Market and Credit Risk -- 1.2 Interest Rate and Credit Risk Correlation -- 1.3 Decomposing Credit Risk -- 2 Interest Rate-Credit Spread Correlations -- 2.1 Spread Data -- 2.2 Long-Horizon Correlations -- 2.3 Non-Parametric Estimates on International Bond Spreads -- 2.4 Non-Parametric Estimates on Bloomberg Spreads -- 3 Market Risk-Rating Transitions Dependencies -- 3.1 Transition Data -- 3.2 Transition Matrices -- 3.3 VaR Calculations -- 4 Conclusion -- References -- Coherent Measures of Risk -- Abstract -- 1 Introduction -- 2 Definition of risk and of coherent risk measures -- 2.1 Risk as the random variable: future net worth -- 2.2 Axioms on Acceptance Sets (Sets of Acceptable Future Net Worths) -- 2.3 Correspondence between Acceptance Sets and Measures of Risk -- 2.4 Correspondence between the Axioms on Acceptance Sets and the Axioms on Measures of Risks -- 3 Three Currently Used Methods of Measuring Market Risk -- 3.1 An Organized Exchange's Rules: The SPAN Computations -- 3.2 Some Model-Free Measures of Risks: the SEC rules on Final Net Worth -- 3.3 Some Model-Dependent Rules based on Quantiles -- 4 Representation Theorems for Coherent Risk Measures -- 4.1 Representation of Coherent Risk Measures by Scenarios.

4.2 Construction of Coherent Risk Measures by Extension of Certain Risk Measurements -- 4.3 Relation between Scenario Probabilities and Pricing Measures -- 5 Two Applications of Representations of Coherent Risk Measures -- 5.1 A Proposal: the 'Worst Conditional Expectation' Measure of Risk -- 5.2 Construction of a Measure Out of Measures on Separate Classes of Risks -- Acknowledgments -- References -- Correlation and Dependence in Risk Management: Properties and Pitfalls -- Abstract -- 1 Introduction -- 1.1 Correlation in finance and insurance -- 1.2 Correlation as a source of confusion -- 1.3 Organization of article -- 2 Copulas -- 2.1 What is a copula? -- 2.2 Examples of copulas -- 2.3 Invariance -- 3 Linear Correlation -- 3.1 What is correlation? -- 3.2 Shortcomings of correlation -- 3.3 Spherical and elliptical distributions -- 3.4 Covariance and elliptical distributions in risk management -- 4 Alternative dependence concepts -- 4.1 Comonotonicity -- 4.2 Desired properties of dependence measures -- 4.3 Rank correlation -- 4.4 Tail Dependence -- 4.5 Concordance -- 5 Fallacies -- 6 Simulation of Random Vectors -- 6.1 Given marginals and linear correlations -- 6.2 Given marginals and Spearman's rank correlations -- 6.3 Given marginals and copula -- 7 Conclusions -- Acknowledgements -- References -- Measuring Risk with Extreme Value Theory -- 1 Introduction -- 2 Outline of Extreme Value Theory -- 3 Bayesian Statistics for Risk Assessment -- 4 Multivariate Extremes -- 5 A Changepoint Model for Stochastic Volatility -- 6 Conclusions -- Acknowledgments -- References -- Extremes in Operational Risk Management -- Abstract -- 1 Introduction -- 2 Firm-wide operational risk management -- 3 Stable random variables and extreme value theory -- 4 Stochastic model for measuring of operational risk -- 5 Simulation of peaks over threshold model parameters by MCMC.

6 Example: bank trading losses analysis through the Russian crisis -- Prediction of actual losses by the economic loss capital provision at firm level -- Economic capital for operational risk at business unit level -- Economic capital for operational risk at firm level -- Conclusions and future directions -- References.