2008 AGI-Information Management Consultants May be used for personal purporses only or by libraries associated to dandelon.com network. Third Edition Philippe Jorion GARP WILEY John Wiley & Sons, Inc.
Contents Preface Introduction xix xxi Part I: Quantitative Analysis 1 Ch. 1 Bond Fundamentals 3 1.1 Discounting, Present Value, and Future Value 4 1.2 Price-Yield Relationship 6 1.2.1 Valuation 6 1.2.2 Taylor Expansion 8 1.3 Bond Price Derivatives 10 1.3.1 Interpreting Duration and Convexity 17 1.3.2 Portfolio Duration and Convexity 24 1.4 Answers to Chapter Examples 27 Ch. 2 Fundamentals of Probability 33 2.1 Characterizing Random Variables 33 2.1.1 Univariate Distribution Functions 34 2.1.2 Moments 36 2.2 Multivariate Distribution Functions 40 2.3 Functions of Random Variables 43 2.3.1 Linear Transformation of Random Variables 43 2.3.2 Sum of Random Variables 44 2.3.3 Portfolios of Random Variables 45 2.3.4 Product of Random Variables 46 2.3.5 Distributions of Transformations of Random Variables. 46 2.4 Important Distribution Functions 49 2.4.1 Uniform Distribution 49 2.4.2 Normal Distribution 50 2.4.3 Lognormal Distribution 53 2.4.4 Student's t Distribution 56 2.4.5 Binomial Distribution 58 2.5 Limit Distributions 60 vn
viii CONTENTS 2.5.1 Distribution of Averages 60 2.5.2 Distribution of Tails 61 2.6 Answers to Chapter Examples 62 Ch. 3 Fundamentals of Statistics 67 3.1 Real Data 68 3.1.1 Measuring Returns 68 3.1.2 Time Aggregation 69 3.1.3 Portfolio Aggregation 71 3.2 Parameter Estimation 74 3.3 Regression Analysis 76 3.3.1 Bivariate Regression 77 3.3.2 Autoregression 79 3.3.3 Multivariate Regression 79 3.3.4 Example 80 3.3.5 Pitfalls with Regressions 82 3.4 Answers to Chapter Examples 85 Ch. 4 Monte Carlo Methods 87 4.1 Simulations with One Random Variable 87 4.1.1 Simulating Markov Processes 88 4.1.2 The Geometric Brownian Motion 88 4.1.3 Simulating Yields 92 4.1.4 Binomial Trees 94 4.2 Implementing Simulations 97 4.2.1 Simulation for VAR 97 4.2.2 Simulation for Derivatives 98 4.2.3 Accuracy 99 4.3 Multiple Sources of Risk 101 4.3.1 The Cholesky Factorization 102 4.3.2 The Curse of Dimensionality 103 4.4 Answers to Chapter Examples 104 Part II: Capital Markets 107 Ch. 5 Introduction to Derivatives 109 5.1 Overview of Derivatives Markets 110 5.2 Forward Contracts Ill 5.2.1 Definition Ill 5.2.2 Valuing Forward Contracts 113 5.2.3 Valuing an Off-Market Forward Contract 116 5.2.4 Valuing Forward Contracts with Income Payments... 117
CONTENTS ix 5.3 Futures Contracts 121 5.3.1 Definitions of Futures 121 5.3.2 Valuing Futures Contracts 123 5.4 Swap Contracts 123 5.5 Answers to Chapter Examples 124 Ch. 6 Options 127 6.1 Option Payoffs 127 6.1.1 Basic Options 127 6.1.2 Put-Call Parity 130 6.1.3 Combination of Options 133 6.2 Option Premiums 136 6.2.1 General Relationships 136 6.2.2 Early Exercise of Options 139 6.3 Valuing Options 141 6.3.1 Pricing by Replication 141 6.3.2 Black-Scholes Valuation 143 6.3.3 Extensions 146 6.3.4 Market versus Model Prices 148 6.4 Other Option Contracts 149 6.5 Valuing Options by Numerical Methods 152 6.6 Answers to Chapter Examples 155 Ch. 7 Fixed-Income Securities 159 7.1 Overview of Debt Markets 159 7.2 Fixed-Income Securities 162 7.2.1 Instrument Types 162 7.2.2 Methods of Quotation 165 7.3 Analysis of Fixed-Income Securities 166 7.3.1 The NPV Approach 166 7.3.2 Pricing 168 7.3.3 Duration 169 7.4 Spot and Forward Rates 171 7.5 Mortgage-Backed Securities 176 7.5.1 Description 176 7.5.2 Prepayment Risk 180 7.5.3 Financial Engineering and CMOs 183 7.6 Answers to Chapter Examples 189 Ch. 8 Fixed-Income Derivatives 193 8.1 Forward Contracts 193 8.2 Futures 196 8.2.1 Eurodollar Futures 196
x CONTENTS 8.2.2 T-Bond Futures 198 8.3 Swaps 201 8.3.1 Instruments 201 8.3.2 Pricing 203 8.4 Options 207 8.4.1 Caps and Floors 207 8.4.2 Swaptions 210 8.4.3 Exchange-Traded Options 212 8.5 Answers to Chapter Examples 213 Ch. 9 Equity, Currency, and Commodity Markets 217 9.1 Equities 218 9.1.1 Overview 218 9.1.2 Valuation 219 9.2 Convertible Bonds and Warrants 221 9.2.1 Definitions 221 9.2.2 Valuation 223 9.3 Equity Derivatives 225 9.3.1 Stock Index Futures 225 9.3.2 Single Stock Futures 228 9.3.3 Equity Options 228 9.3.4 Equity Swaps 229 9.4 Currency Markets 229 9.5 Currency Swaps 231 9.5.1 Instruments 231 9.5.2 Pricing 233 9.6 Commodities 236 9.6.1 Products 236 9.6.2 Pricing of Futures 237 9.6.3 Futures and Expected Spot Prices 239 9.7 Answers to Chapter Examples 243 Part III: Market Risk Management 247 Ch. 10 Introduction to Market Risk Measurement 249 10.1 Introduction to Financial Market Risks 250 10.1.1 Types of Financial Risks 250 10.1.2 Risk Management Tools 251 10.2 VAR as a Downside Risk Measure 252 10.2.1 VAR: Definition 252 10.2.2 VAR: Caveats... 255 10.2.3 Alternative Measures of Risk 257 10.2.4 Cash Flow at Risk. 259
CONTENTS xi 10.3 VAR Parameters 260 10.3.1 Confidence Level 260 10.3.2 Horizon 261 10.3.3 Application: The Basel Rules 263 10.4 Elements of VAR Systems 264 10.4.1 Portfolio Positions 264 10.4.2 Risk Factors 265 10.4.3 VAR Methods 265 10.5 Stress Testing 266 10.6 Liquidity Risk 269 10.7 Answers to Chapter Examples 272 Ch. 11 Sources of Market Risk 277 11.1 Sources of Loss: A Decomposition 277 11.2 Currency Risk 279 11.2.1 Currency Volatility 280 11.2.2 Correlations 281 11.2.3 Cross-Rate Volatility 282 11.3 Fixed-Income Risk 283 11.3.1 Factors Affecting Yields 283 11.3.2 Bond Price and Yield Volatility 285 11.3.3 Correlations 288 11.3.4 Global Interest Rate Risk 289 11.3.5 Real Yield Risk 291 11.3.6 Credit Spread Risk 292 11.3.7 Prepayment Risk 292 11.4 Equity Risk 294 11.4.1 Stock Market Volatility 294 11.5 Commodity Risk 296 11.5.1 Commodity Volatility 296 11.5.2 Futures Risk 296 11.6 Risk Simplification 300 11.6.1 Diagonal Model 300 11.6.2 Fixed-Income Portfolio Risk 301 11.7 Answers to Chapter Examples 303 Ch. 12 Hedging Linear Risk 307 12.1 Introduction to Futures Hedging 308 1-2.1.1 Unitary Hedging 308 12.1.2 Basis Risk 310 12.2 Optimal Hedging 312 12.2.1 The Optimal Hedge Ratio 312 12.2.2 Example 315
xii CONTENTS 12.2.3 Liquidity Issues 317 12.3 Applications for Optimal Hedging 318 12.3.1 Duration Hedging 318 12.3.2 Beta Hedging 321 12.4 Answers to Chapter Examples 323 Ch. 13 Nonlinear Risk: Options 325 13.1 Evaluating Options 326 13.1.1 Definitions 326 13.1.2 Taylor Expansion 327 13.1.3 Option Pricing 328 13.2 Option "Greeks" 330 13.2.1 Option Sensitivities: Delta and Gamma 330 13.2.2 Option Sensitivities: Vega 333 13.2.3 Option Sensitivities: Rho 335 13.2.4 Option Sensitivities: Theta 336 13.2.5 Option Pricing and the "Greeks" 336 13.2.6 Option Sensitivities: Summary 339 13.3 Dynamic Hedging 342 13.3.1 Delta and Dynamic Hedging 343 13.3.2 Implications 344 13.3.3 Distribution of Option Payoffs 345 13.4 Answers to Chapter Examples 348 Ch. 14 Modeling Risk Factors 351 14.1 Normal and Lognormal Distributions 352 14.1.1 Why the Normal? 352 14.1.2 Computing Returns 352 14.1.3 Time Aggregation 354 14.2 Fat Tails 356 14.3 Time Variation in Risk 358 14.3.1 GARCH 359 14.3.2 EWMA 361 14.3.3 Option Data 364 14.3.4 Implied Distributions 365 14.4 Answers to Chapter Examples 367 Ch. 15 VAR Methods 369 15.1 VAR: Local versus Full Valuation 370 15.1.1 Local Valuation 370 15.1.2 Full Valuation 371 15.1.3 Delta-Gamma Method. 372 15.2 VAR Methods: Overview 374
CONTENTS xiii 15.2.1 Mapping 374 15.2.2 Delta-Normal Method 375 15.2.3 Historical-Simulation Method 375 15.2.4 Monte Carlo Simulation Method 376 15.2.5 Comparison of Methods 377 15.3 Example 379 15.3.1 Mark-to-Market 379 15.3.2 Risk Factors 380 15.3.3 VAR: Historical Simulation 382 15.3.4 VAR: Delta-Normal Method 384 15.4 Answers to Chapter Examples 386 Part IV: Investment and Risk Management 389 Ch. 16 Portfolio Management 391 16.1 Institutional Investors 392 16.2 Portfolio Management 393 16.2.1 Risk Measurement 393 16.2.2 Performance Measurement 395 16.2.3 Performance Attribution 396 16.2.4 Performance Evaluation and Survivorship 399 16.3 Risk Budgeting 401 16.4 Answers to Chapter Examples 403 Ch. 17 Hedge Fund Risk Management 407 17.1 The Hedge Fund Industry 408 17.2 Leverage, and Long and Short Positions 409 17.2.1 Long Position 409 17.2.2 Short Position 410 17.2.3 Long and Short Positions 411 17.3 Hedge Fund Risk Management 413 17.3.1 Types of Market Risk 413 17.3.2 Hedge Fund Styles 414 17.3.3 Liquidity and Model Risk 422 17.4 Hedge Fund Transparency 424 17.5 Answers to Chapter Examples 428 Part V: Credit Risk Management 431 Ch. 18 Introduction to Credit Risk 433 18.1 Settlement Risk 434 18.1.1 Presettlement versus Settlement Risk 434
xiv CONTENTS 18.1.2 Handling Settlement Risk 434 18.2 Overview of Credit Risk 436 18.2.1 Drivers of Credit Risk 436 18.2.2 Measurement of Credit Risk 437 18.2.3 Credit Risk versus Market Risk 438 18.3 Measuring Credit Risk 439 18.3.1 Credit Losses 439 18.3.2 Joint Events 439 18.3.3 An Example 441 18.4 Credit Risk Diversification 445 18.5 Answers to Chapter Examples 449 Ch. 19 Measuring Actuarial Default Risk 451 19.1 Credit Event 452 19.2 Default Rates 454 19.2.1 Credit Ratings 454 19.2.2 Historical Default Rates 457 19.2.3 Cumulative and Marginal Default Rates 460 19.2.4 Transition Probabilities 465 19.2.5 Time Variation in Default Probabilities 467 19.3 Recovery Rates 467 19.3.1 The Bankruptcy Process 468 19.3.2 Estimates of Recovery Rates 469 19.4 Application to Portfolio Rating 472 19.5 Assessing Corporate and Sovereign Rating 475 19.5.1 Corporate Default 475 19.5.2 Sovereign Default 476 19.6 Answers to Chapter Examples 479 Ch. 20 Measuring Default Risk from Market Prices 483 20.1 Corporate Bond Prices 484 20.1.1 Spreads and Default Risk 484 20.1.2 Risk Premium 486 20.1.3 The Cross-Section of Yield Spreads 487 20.1.4 Time Variation in Credit Spreads 490 20.2 Equity Prices 491 20.2.1 The Merton Model 491 20.2.2 Pricing Equity and Debt 493 20.2.3 Applying the Merton Model 495 20.2.4 Example 498 20.3 Answers to Chapter Examples 499
CONTENTS xv Ch. 21 Credit Exposure 501 21.1 Credit Exposure by Instrument 502 21.2 Distribution of Credit Exposure 504 21.2.1 Expected and Worst Exposure 504 21.2.2 Time Profile 506 21.2.3 Exposure Profile for Interest Rate Swaps 506 21.2.4 Exposure Profile for Currency Swaps 515 21.2.5 Exposure Profile for Different Coupons 517 21.3 Exposure Modifiers 519 21.3.1 Marking to Market 519 21.3.2 Exposure Limits 521 21.3.3 Recouponing 521 21.3.4 Netting Arrangements 523 21.4 Credit Risk Modifiers 527 21.4.1 Credit Triggers 527 21.4.2 Time Puts 528 21.5 Answers to Chapter Examples 528 Ch. 22 Credit Derivatives 531 22.1 Introduction 531 22.2 Types of Credit Derivatives 532 22.2.1 Credit Default Swaps 533 22.2.2 Total-Return Swaps 536 22.2.3 Credit Spread Forwards and Options 538 22.2.4 Credit-Linked Notes 539 22.3 Pricing and Hedging Credit Derivatives 542 22.3.1 Methods 542 22.3.2 Example: Credit Default Swap 542 22.4 Pros and Cons of Credit Derivatives 545 22.5 Answers to Chapter Examples 547 Ch. 23 Managing Credit Risk 551 23.1 Measuring the Distribution of Credit Losses 552 23.2 Measuring Expected Credit Loss 555 23.2.1 Expected Losses over a Target Horizon 555 23.2.2 The Time Profile of Expected Loss 556. 23.3 Measuring Credit VAR 558 23.4 Portfolio Credit Risk Models 560 23.4.1 Approaches to Portfolio Credit Risk Models 560 23.4.2 CreditMetrics 562 23.4.3 CreditRisk+ 565 23.4.4 Moody's KMV 565 23.4.5 Credit Portfolio View 566
xvi CONTENTS 23.4.6 Comparison 567 23.5 Answers to Chapter Examples 570 Part VI: Operational and Integrated Risk Management 573 Ch. 24 Operational Risk 575 24.1 The Importance of Operational Risk 576 24.1.1 Case Histories 576 24.1.2 Business Lines 577 24.2 Identifying Operational Risk 578 24.3 Assessing Operational Risk 581 24.3.1 Comparison of Approaches 581 24.3.2 Actuarial Models 582 24.4 Managing Operational Risk 586 24.4.1 Capital Allocation and Insurance 586 24.4.2 Mitigating Operational Risk 588 24.4.3 Conceptual Issues 590 24.5 Answers to Chapter Examples 591 Ch. 25 Risk Capital and RAROC 595 25.1 RAROC 596 25.1.1 Risk Capital 596 25.1.2 RAROC Methodology 597 25.1.3 Application to Compensation 598 25.2 Performance Evaluation and Pricing 600 25.3 Answers to Chapter Examples 602 Ch. 26 Best Practices Reports 603 26.1 The G-30 Report 603 26.2 The Bank of England Report on Barings 606 26.3 The CRMPG Report on LTCM 607 26.4 Answer to Chapter Example 609 Ch. 27 Firm-Wide Risk Management 611 27.1 Integrated Risk Management 612 27.1.1 Types of Risk 612 27.1.2 Risk Interactions 612 27.2 Three-Pillar Framework 614 27.2.1 Best-Practices Policies 614 27.2.2 Best-Practices Methodologies 615
CONTENTS xvii 27.2.3 Best-Practices Infrastructure 615 27.3 Organizational Structure 615 27.4 Controlling Traders 620 27.4.1 Trader Compensation 620 27.4.2 Trader Limits 621 27.5 Answers to Chapter Examples 624 Part VII: Legal, Accounting, and Tax Risk Management 627 Ch, 28 Legal Issues 62» 28,! Legal Risks with Derivatives,,,,,..,..,, ;,.,.,, 630 28.2 Netting 633 28.2.1 Netting under the Basel Accord 634 28.2.2 Walk-Away Clauses 635 28.2.3 Netting and Exchange Margins 635 28.3 ISDA Master Netting Agreement 636 28.4 The 2002 Sarbanes-Oxley Act 639 28.5 Glossary 641 28.5.1 General Legal Terms 641 28.5.2 Bankruptcy Terms 641 28.5.3 Contract Terms 642 28.6 Answers to Chapter Examples 643 Ch. 29 Accounting and Tax Issues 645 29.1 Internal Reporting 646 29.1.1 Purpose of Internal Reporting 646 29.1.2 Comparison of Methods 647 29.2 Major Issues in Reporting 648 29.2.1 Valuation Issues 648 29.2.2 Reporting Method for Derivatives 650 29.3 External Reporting: FASB 652 29.3.1 FAS 133 652 29.3.2 Definition of Derivative 653 29.3.3 Embedded Derivative 654 29.3.4 Disclosure Rules 655 29.3.5 Hedge Effectiveness 657 29.3.6 General Evaluation of FAS 133 658 29.3.7 Accounting Treatment of SPEs 659 29.4 External Reporting: IASB 661 29.4.1 IAS 39 662 29.5 Tax Considerations 664 29.6 Answers to Chapter Examples 665
xviii CONTENTS Part VIII: Regulation and Compliance 667 Ch. 30 Regulation of Financial Institutions 669 30.1 Definition of Financial Institutions 669 30.2 Systemic Risk 671 30.3 Regulation of Commercial Banks 672 30.4 Regulation of Securities Houses 675 30.5 Tools and Objectives of Regulation 677 30.6 Answers to Chapter Examples 679 Ch. 31 The Basel Accord 681 31.1 Steps in the Basel Accord 682 31.1.1 The Basel I Accord 682 31.1.2 The 1996 Amendment 682 31.1.3 The Basel II Accord 683 31.2 The 1988 Basel Accord 685 31.2.1 Risk Capital 685 31.2.2 On-Balance Sheet Risk Charges 688 31.2.3 Off-Balance Sheet Risk Charges 689 31.2.4 Total Risk Charge 694 31.3 Illustration 695 31.4 The New Basel Accord 698 31.4.1 Issues with the 1988 Basel Accord 698 31.4.2 Definition of Capital 699 31.4.3 The Credit Risk Charge 700 31.4.4 The Operational Risk Charge 704 31.4.5 Evaluation 705 31.5 Conclusions 706 31.6 Answers to Chapter Examples 707 Ch. 32 The Basel Market Risk Charges 711 32.1 The Standardized Method 711 32.2 The Internal Models Approach 713 32.2.1 Qualitative Requirements 713 32.2.2 The Market Risk Charge 714 32.2.3 Combination of Approaches 716 32.3 Stress Testing 719 32.4 Backtesting 721 32.4.1 Measuring Exceptions 721 32.4.2 Statistical Decision Rules 722 32.4.3 The Penalty Zones. 722 32.5 Answers to Chapter Examples 725 Index 729