Moorad Choudhry is an MD in Group Treasury at The Royal Bank of Scotland. He is Visiting Professor at the Department of Mathematical Sciences, Brunel University, Visiting Professor at the IFS-School of Finance, Visiting Teaching Fellow at the Department of Management, Birkbeck, University of London, Vice-Chair of the Board of Directors of PRMIA, and Fellow of the Chartered Institute for Securities & Investment.

• Foreword xvPreface xviiPreface to the first edition xxiAbout the author xxiii1 Introduction to Risk 1Defining risk 2The elements of risk: characterising risk 3Forms of market risk 4Other risks 5Risk estimation 6Risk management 7The risk management function 7Managing risk 9Quantitative measurement of risk–reward 9Standard deviation 10Sharpe Ratio 10Van Ratio 112 Volatility and Correlation 13Statistical concepts 14Arithmetic mean 14Probability distributions 16Confidence intervals 18Volatility 20The normal distribution and VaR 26Correlation 283 Value-at-risk 29What is VaR? 30Definition 30Methodology 32Centralised database 32Correlation assumptions 33Correlation method 33Historical simulation method 34Monte Carlo simulation method 35Validity of the volatility-correlation VaR estimate 35How to calculate VaR 35Historical method 36Simulation method 37Variance–covariance, analytic or parametric method 37Mapping 44Confidence intervals 47Comparison between methods 48Choosing between methods 48Comparison with the historical approach 53Comparing VaR calculation for different methodologies 54Summary 564 Value-at-risk for Fixed Interest Instruments 59Fixed income products 60Bond valuation 60Duration 62Modified duration 64Convexity 64Interest rate products 65Forward rate agreements 65Fixed income portfolio 68Applying VaR for a FRA 70VaR for an interest rate swap 72Applying VaR for a bond futures contract 76Calculation illustration 76The historical method 79Simulation methodology 80Volatility over time 81Application 81Bloomberg screens 825 Options: Risk and Value-at-risk 85Option valuation using the Black–Scholes model 86Option pricing 86Volatility 88The Greeks 89Delta 90Gamma 90Vega 91Other Greeks 92Risk measurement 92Spot ladder 93Maturity ladder 93Across-time ladder 93Jump risk 93Applying VaR for Options 946 Monte Carlo Simulation and Value-at-risk 99Introduction: Monte Carlo simulation 100Option value under Monte Carlo 100Monte Carlo distribution 103Monte Carlo simulation and VaR 1047 Regulatory Issues and Stress-testing 107Capital adequacy 108Model compliance 108Cad II 109Specific risk 111Back-testing 112Stress-testing 112Simulating stress 113Stress-testing in practice 114Issues in stress-testing 115The Crash and Basel III 116Stressed VaR 1168 Credit Risk and Credit Value-at-risk 119Types of credit risk 120Credit spread risk 120Credit default risk 121Credit ratings 121Credit ratings 121Ratings changes over time 123Corporate recovery rates 125Credit derivatives 126Measuring risk for a CDS contract 128Modelling credit risk 129Time horizon 131Data inputs 131CreditMetrics 131Methodology 132Time horizon 133Calculating the credit VaR 134CreditRisk þ 137Applications of credit VaR 142Prioritising risk-reducing actions 142Standard credit limit setting 143Concentration limits 144Integrating the credit risk and market risk functions 1449 A Review of Value-at-risk 147VaR in Crisis 149Weaknesses Revealed 151Market risk 151Credit risk 153Portfolio effects 155New Regulation and Development 158Procyclicality: stressed VaR (SVaR) 158Default and migration risks: incremental risk charge (IRC) 159Liquidity risks: differing liquidity horizons 161Counterparty risks: CVA VaR 162Fat tail risk: over-buffering 164New framework for trading book 164Beyond the Current Paradigm 166Exercises 171Appendix: Taylor’s Expansion 179Abbreviations 183Selected bibliography 185Index 187