ANDREA RESTI, formerly an officer at one of Italy's largest banks, has worked on Basel II issues for the Centre for European Policy Studies (Brussels). A consultant to several major banks, as well as to the Bank of Italy, he has held courses on credit risk for GARP and PRMIA.

ANDREA SIRONI, formerly with Chase Manhattan Bank in London, has been a visiting scholar at the Stern School of Business (NYU) and at the Federal Reserve Board of Governors (Washington). He is currently Dean for International Affairs at Bocconi University (Milan) and a member of the Fitch Academic Advisory Board.

The authors are both professors of Financial Markets and Institutions at Bocconi and have been teaching banking and finance for more than 15 years. Their publications comprise many articles in major international academic journals, as well as several risk management and banking textbooks, including a best-selling title on recovery risk.

Foreword xix

Motivation and Scope of this Book: A Quick Guided Tour xxi

Part I Interest Rate Risk 1

Introduction to Part I 3

1 The Repricing Gap Model 9

1.1 Introduction 9

1.2 The gap concept 9

1.3 The maturity-adjusted gap 12

1.4 Marginal and cumulative gaps 15

1.5 The limitations of the repricing gap model 19

1.6 Some possible solutions 20

Selected Questions and Exercises 25

Appendix 1A The Term Structure of Interest Rates 28

Appendix 1B Forward Rates 32

2 The Duration Gap Model 35

2.1 Introduction 35

2.2 Towards mark-to-market accounting 35

2.3 The duration of financial instruments 39

2.4 Estimating the duration gap 42

2.5 Problems of the duration gap model 45

Selected Questions and Exercises 47

Appendix 2A The Limits of Duration 49

3 Models Based on Cash-Flow Mapping 57

3.1 Introduction 57

3.2 The objectives of cash-flow mapping and term structure 57

3.3 Choosing the vertices of the term structure 58

3.4 Techniques based on discrete intervals 59

3.5 Clumping 64

3.6 Concluding comments 68

Selected Questions and Exercises 69

Appendix 3A Estimating the Zero-Coupon Curve 71

4 Internal Transfer Rates 77

4.1 Introduction 77

4.2 Building an ITR system: a simplified example 77

4.3 Single and multiple ITRs 79

4.4 Setting internal interest transfer rates 84

4.5 ITRs for transactions with embedded options 88

4.6 Summary: the ideal features of an ITR system 93

Selected Questions and Exercises 94

Appendix 4A Derivative Contracts on Interest Rates 96

Part II Market Risks 103

Introduction to Part II 105

5 The Variance-Covariance Approach 115

5.1 Introduction 115

5.2 VaR derivation assuming normal return distribution 115

5.3 Sensitivity of portfolio positions to market factors 126

5.4 Mapping of risk positions 133

5.5 Summary of the variance-covariance approach and main limitations 143

Selected Questions and Exercises 151

Appendix 5A Stockmarket Betas 154

Appendix 5B Option Sensitivity Coefficients: "Greeks" 157

6 Volatility Estimation Models 163

6.1 Introduction 163

6.2 Volatility estimation based upon historical data: simple moving averages 163

6.3 Volatility estimation based upon historical data: exponential moving averages 167

6.4 Volatility prediction: GARCH models 172

6.5 Volatility prediction: implied volatility 179

6.6 Covariance and correlation estimation 181

Selected Questions and Exercises 182

7 Simulation Models 185

7.1 Introduction 185

7.2 Historical simulations 189

7.3 Monte Carlo simulations 205

7.4 Stress testing 218

Selected Questions and Exercises 221

8 Evaluating VaR Models 225

8.1 Introduction 225

8.2 An example of backtesting: a stock portfolio VaR 225

8.3 Alternative VaR model backtesting techniques 232

Selected Questions and Exercises 244

Appendix 8A VaR Model Backtesting According to the Basel Committee 246

9 VaR Models: Summary, Applications and Limitations 251

9.1 Introduction 251

9.2 A summary overview of the different models 251

9.3 Applications of VaR models 253

9.4 Six "False Shortcomings" of VaR 260

9.5 Two real problems of VaR models 263

9.6 An Alternative Risk Measure: Expected Shortfall (ES) 268

Selected Questions and Exercises 269

Appendix 9A Extreme Value Theory 272

Part III Credit Risk 275

Introduction to Part III 277

10 Credit-Scoring Models 287

10.1 Introduction 287

10.2 Linear discriminant analysis 287

10.3 Regression models 299

10.4 Inductive models 301

10.5 Uses, limitations and problems of credit-scoring models 307

Selected Questions and Exercises 309

Appendix 10A The Estimation of the Gamma Coefficients in Linear Discriminant Analysis 311

11 Capital Market Models 313

11.1 Introduction 313

11.2 The approach based on corporate bond spreads 313

11.3 Structural models based on stock prices 321

Selected Questions and Exercises 340

Appendix 11A Calculating the Fair Spread on a Loan 342

Appendix 11B Real and Risk-Neutral Probabilities of Default 343

12 LGD and Recovery Risk 345

12.1 Introduction 345

12.2 What factors drive recovery rates? 346

12.3 The estimation of recovery rates 347

12.4 From past data to LGD estimates 351

12.5 Results from selected empirical studies 353

12.6 Recovery risk 356

12.7 The link between default risk and recovery risk 358

Selected Questions and Exercises 362

Appendix 12A The Relationship between PD and RR in the Merton model 364

13 Rating Systems 369

13.1 Introduction 369

13.2 Rating assignment 370

13.3 Rating quantification 379

13.4 Rating validation 388

Selected Questions and Exercises 398

14 Portfolio Models 401

14.1 Introduction 401

14.2 Selecting time horizon and confidence level 402

14.3 The migration approach: CreditMetricsTM 406

14.4 The structural approach: PortfolioManagerTM 423

14.5 The macroeconomic approach: CreditPortfolioViewTM 426

14.6 The actuarial approach: CreditRisk+TM 428

14.7 A brief comparison of the main models 439

14.8 Some limitations of the credit risk models 442

Selected Questions and Exercises 446

Appendix 14A Asset correlation versus default correlation 449

15 Some Applications of Credit Risk Measurement Models 451

15.1 Introduction 451

15.2 Loan pricing 451

15.3 Risk-adjusted performance measurement 457

15.4 Setting limits on risk-taking units 459

15.5 Optimizing the composition of the loan portfolio 461

Selected Questions and Exercises 462

Appendix 15A Credit Risk Transfer Tools 464

16 Counterparty Risk on OTC Derivatives 473

16.1 Introduction 473

16.2 Settlement and pre-settlement risk 474

16.3 Estimating pre-settlement risk 474

16.4 Risk-adjusted performance measurement 495

16.5 Risk-mitigation tools for pre-settlement risk 496

Selected Questions and Exercises 504

Part IV Operational Risk 505

Introduction to Part IV 507

17 Operational Risk: Definition, Measurement and Management 511

17.1 Introduction 511

17.2 OR: How can we define it? 512

17.3 Measuring OR 517

17.4 Towards an OR management system 533

17.5 Final remarks 535

Selected Questions and Exercises 537

Appendix 17A OR measurement and EVT 539

Part V Regulatory Capital Requirements 543

Introduction to Part V 545

18 The 1988 Capital Accord 547

18.1 Introduction 547

18.2 The capital ratio 549

18.3 Shortcomings of the capital adequacy framework 555

18.4 Conclusions 559

Selected Questions and Exercises 559

Appendix 18A The Basel Committee 563

19 The Capital Requirements for Market Risks 565

19.1 Introduction 565

19.2 Origins and characteristics of capital requirements 565

19.3 The capital requirement on debt securities 568

19.4 Positions in equity securities: specific and generic requirements 575

19.5 The requirement for positions in foreign currencies 576

19.6 The requirement for commodity positions 578

19.7 The use of internal models 578

Selected Questions and Exercises 585

Appendix 19A Capital Requirements Related to Settlement, Counterparty and Concentration Risks 588

20 The New Basel Accord 591

20.1 Introduction 591

20.2 Goals and Contents of the Reform 591

20.3 Pillar One: The Standard Approach to Credit Risk 593

20.4 The Internal Ratings-based Approach 597

20.5 Pillar Two: A New Role for Supervisory Authorities 612

20.6 Pillar Three: Market Discipline 614

20.7 Pros and Cons of Basel II 616

20.8 the Impact of Basel II 619

Selected Questions and Exercises 630

21 Capital Requirements on Operational Risk 633

21.1 Introduction 633

21.2 The capital requirement on operational risk 633

21.3 Weaknesses of the 2004 Accord 645

21.4 Final remarks 647

Selected Questions and Exercises 647

Part VI Capital Management and Value Creation 651

Introduction to Part VI 653

22 Capital Management 657

22.1 Introduction 657

22.2 Defining and measuring capital 658

22.3 Optimizing regulatory capital 675

22.4 Other instruments not included within regulatory capital 685

Selected Questions and Exercises 691

23 Capital Allocation 693

23.1 Introduction 693

23.2 Measuring capital for the individual business units 694

23.3 The relationship between allocated capital and total capital 702

23.4 Capital allocated and capital absorbed 712

23.5 Calculating risk-adjusted performance 715

23.6 Optimizing the allocation of capital 722

23.7 The organizational aspects of the capital allocation process 726

Selected Questions and Exercises 728

Appendix 23A The Correlation Approach 730

Appendix 23B The Virtual Nature of Capital Allocation 731

24 Cost of Capital and Value Creation 735

24.1 Introduction 735

24.2 The link between Risk Management and Capital Budgeting 735

24.3 Capital...