Third Edition. Philippe Jorion GARP. WILEY John Wiley & Sons, Inc.
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1 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.
2 Contents Preface Introduction xix xxi Part I: Quantitative Analysis 1 Ch. 1 Bond Fundamentals Discounting, Present Value, and Future Value Price-Yield Relationship Valuation Taylor Expansion Bond Price Derivatives Interpreting Duration and Convexity Portfolio Duration and Convexity Answers to Chapter Examples 27 Ch. 2 Fundamentals of Probability Characterizing Random Variables Univariate Distribution Functions Moments Multivariate Distribution Functions Functions of Random Variables Linear Transformation of Random Variables Sum of Random Variables Portfolios of Random Variables Product of Random Variables Distributions of Transformations of Random Variables Important Distribution Functions Uniform Distribution Normal Distribution Lognormal Distribution Student's t Distribution Binomial Distribution Limit Distributions 60 vn
3 viii CONTENTS Distribution of Averages Distribution of Tails Answers to Chapter Examples 62 Ch. 3 Fundamentals of Statistics Real Data Measuring Returns Time Aggregation Portfolio Aggregation Parameter Estimation Regression Analysis Bivariate Regression Autoregression Multivariate Regression Example Pitfalls with Regressions Answers to Chapter Examples 85 Ch. 4 Monte Carlo Methods Simulations with One Random Variable Simulating Markov Processes The Geometric Brownian Motion Simulating Yields Binomial Trees Implementing Simulations Simulation for VAR Simulation for Derivatives Accuracy Multiple Sources of Risk The Cholesky Factorization The Curse of Dimensionality Answers to Chapter Examples 104 Part II: Capital Markets 107 Ch. 5 Introduction to Derivatives Overview of Derivatives Markets Forward Contracts Ill Definition Ill Valuing Forward Contracts Valuing an Off-Market Forward Contract Valuing Forward Contracts with Income Payments
4 CONTENTS ix 5.3 Futures Contracts Definitions of Futures Valuing Futures Contracts Swap Contracts Answers to Chapter Examples 124 Ch. 6 Options Option Payoffs Basic Options Put-Call Parity Combination of Options Option Premiums General Relationships Early Exercise of Options Valuing Options Pricing by Replication Black-Scholes Valuation Extensions Market versus Model Prices Other Option Contracts Valuing Options by Numerical Methods Answers to Chapter Examples 155 Ch. 7 Fixed-Income Securities Overview of Debt Markets Fixed-Income Securities Instrument Types Methods of Quotation Analysis of Fixed-Income Securities The NPV Approach Pricing Duration Spot and Forward Rates Mortgage-Backed Securities Description Prepayment Risk Financial Engineering and CMOs Answers to Chapter Examples 189 Ch. 8 Fixed-Income Derivatives Forward Contracts Futures Eurodollar Futures 196
5 x CONTENTS T-Bond Futures Swaps Instruments Pricing Options Caps and Floors Swaptions Exchange-Traded Options Answers to Chapter Examples 213 Ch. 9 Equity, Currency, and Commodity Markets Equities Overview Valuation Convertible Bonds and Warrants Definitions Valuation Equity Derivatives Stock Index Futures Single Stock Futures Equity Options Equity Swaps Currency Markets Currency Swaps Instruments Pricing Commodities Products Pricing of Futures Futures and Expected Spot Prices Answers to Chapter Examples 243 Part III: Market Risk Management 247 Ch. 10 Introduction to Market Risk Measurement Introduction to Financial Market Risks Types of Financial Risks Risk Management Tools VAR as a Downside Risk Measure VAR: Definition VAR: Caveats Alternative Measures of Risk Cash Flow at Risk. 259
6 CONTENTS xi 10.3 VAR Parameters Confidence Level Horizon Application: The Basel Rules Elements of VAR Systems Portfolio Positions Risk Factors VAR Methods Stress Testing Liquidity Risk Answers to Chapter Examples 272 Ch. 11 Sources of Market Risk Sources of Loss: A Decomposition Currency Risk Currency Volatility Correlations Cross-Rate Volatility Fixed-Income Risk Factors Affecting Yields Bond Price and Yield Volatility Correlations Global Interest Rate Risk Real Yield Risk Credit Spread Risk Prepayment Risk Equity Risk Stock Market Volatility Commodity Risk Commodity Volatility Futures Risk Risk Simplification Diagonal Model Fixed-Income Portfolio Risk Answers to Chapter Examples 303 Ch. 12 Hedging Linear Risk Introduction to Futures Hedging Unitary Hedging Basis Risk Optimal Hedging The Optimal Hedge Ratio Example 315
7 xii CONTENTS Liquidity Issues Applications for Optimal Hedging Duration Hedging Beta Hedging Answers to Chapter Examples 323 Ch. 13 Nonlinear Risk: Options Evaluating Options Definitions Taylor Expansion Option Pricing Option "Greeks" Option Sensitivities: Delta and Gamma Option Sensitivities: Vega Option Sensitivities: Rho Option Sensitivities: Theta Option Pricing and the "Greeks" Option Sensitivities: Summary Dynamic Hedging Delta and Dynamic Hedging Implications Distribution of Option Payoffs Answers to Chapter Examples 348 Ch. 14 Modeling Risk Factors Normal and Lognormal Distributions Why the Normal? Computing Returns Time Aggregation Fat Tails Time Variation in Risk GARCH EWMA Option Data Implied Distributions Answers to Chapter Examples 367 Ch. 15 VAR Methods VAR: Local versus Full Valuation Local Valuation Full Valuation Delta-Gamma Method VAR Methods: Overview 374
8 CONTENTS xiii Mapping Delta-Normal Method Historical-Simulation Method Monte Carlo Simulation Method Comparison of Methods Example Mark-to-Market Risk Factors VAR: Historical Simulation VAR: Delta-Normal Method Answers to Chapter Examples 386 Part IV: Investment and Risk Management 389 Ch. 16 Portfolio Management Institutional Investors Portfolio Management Risk Measurement Performance Measurement Performance Attribution Performance Evaluation and Survivorship Risk Budgeting Answers to Chapter Examples 403 Ch. 17 Hedge Fund Risk Management The Hedge Fund Industry Leverage, and Long and Short Positions Long Position Short Position Long and Short Positions Hedge Fund Risk Management Types of Market Risk Hedge Fund Styles Liquidity and Model Risk Hedge Fund Transparency Answers to Chapter Examples 428 Part V: Credit Risk Management 431 Ch. 18 Introduction to Credit Risk Settlement Risk Presettlement versus Settlement Risk 434
9 xiv CONTENTS Handling Settlement Risk Overview of Credit Risk Drivers of Credit Risk Measurement of Credit Risk Credit Risk versus Market Risk Measuring Credit Risk Credit Losses Joint Events An Example Credit Risk Diversification Answers to Chapter Examples 449 Ch. 19 Measuring Actuarial Default Risk Credit Event Default Rates Credit Ratings Historical Default Rates Cumulative and Marginal Default Rates Transition Probabilities Time Variation in Default Probabilities Recovery Rates The Bankruptcy Process Estimates of Recovery Rates Application to Portfolio Rating Assessing Corporate and Sovereign Rating Corporate Default Sovereign Default Answers to Chapter Examples 479 Ch. 20 Measuring Default Risk from Market Prices Corporate Bond Prices Spreads and Default Risk Risk Premium The Cross-Section of Yield Spreads Time Variation in Credit Spreads Equity Prices The Merton Model Pricing Equity and Debt Applying the Merton Model Example Answers to Chapter Examples 499
10 CONTENTS xv Ch. 21 Credit Exposure Credit Exposure by Instrument Distribution of Credit Exposure Expected and Worst Exposure Time Profile Exposure Profile for Interest Rate Swaps Exposure Profile for Currency Swaps Exposure Profile for Different Coupons Exposure Modifiers Marking to Market Exposure Limits Recouponing Netting Arrangements Credit Risk Modifiers Credit Triggers Time Puts Answers to Chapter Examples 528 Ch. 22 Credit Derivatives Introduction Types of Credit Derivatives Credit Default Swaps Total-Return Swaps Credit Spread Forwards and Options Credit-Linked Notes Pricing and Hedging Credit Derivatives Methods Example: Credit Default Swap Pros and Cons of Credit Derivatives Answers to Chapter Examples 547 Ch. 23 Managing Credit Risk Measuring the Distribution of Credit Losses Measuring Expected Credit Loss Expected Losses over a Target Horizon The Time Profile of Expected Loss Measuring Credit VAR Portfolio Credit Risk Models Approaches to Portfolio Credit Risk Models CreditMetrics CreditRisk Moody's KMV Credit Portfolio View 566
11 xvi CONTENTS Comparison Answers to Chapter Examples 570 Part VI: Operational and Integrated Risk Management 573 Ch. 24 Operational Risk The Importance of Operational Risk Case Histories Business Lines Identifying Operational Risk Assessing Operational Risk Comparison of Approaches Actuarial Models Managing Operational Risk Capital Allocation and Insurance Mitigating Operational Risk Conceptual Issues Answers to Chapter Examples 591 Ch. 25 Risk Capital and RAROC RAROC Risk Capital RAROC Methodology Application to Compensation Performance Evaluation and Pricing Answers to Chapter Examples 602 Ch. 26 Best Practices Reports The G-30 Report The Bank of England Report on Barings The CRMPG Report on LTCM Answer to Chapter Example 609 Ch. 27 Firm-Wide Risk Management Integrated Risk Management Types of Risk Risk Interactions Three-Pillar Framework Best-Practices Policies Best-Practices Methodologies 615
12 CONTENTS xvii Best-Practices Infrastructure Organizational Structure Controlling Traders Trader Compensation Trader Limits Answers to Chapter Examples 624 Part VII: Legal, Accounting, and Tax Risk Management 627 Ch, 28 Legal Issues 62» 28,! Legal Risks with Derivatives,,,,,..,..,, ;,.,.,, Netting Netting under the Basel Accord Walk-Away Clauses Netting and Exchange Margins ISDA Master Netting Agreement The 2002 Sarbanes-Oxley Act Glossary General Legal Terms Bankruptcy Terms Contract Terms Answers to Chapter Examples 643 Ch. 29 Accounting and Tax Issues Internal Reporting Purpose of Internal Reporting Comparison of Methods Major Issues in Reporting Valuation Issues Reporting Method for Derivatives External Reporting: FASB FAS Definition of Derivative Embedded Derivative Disclosure Rules Hedge Effectiveness General Evaluation of FAS Accounting Treatment of SPEs External Reporting: IASB IAS Tax Considerations Answers to Chapter Examples 665
13 xviii CONTENTS Part VIII: Regulation and Compliance 667 Ch. 30 Regulation of Financial Institutions Definition of Financial Institutions Systemic Risk Regulation of Commercial Banks Regulation of Securities Houses Tools and Objectives of Regulation Answers to Chapter Examples 679 Ch. 31 The Basel Accord Steps in the Basel Accord The Basel I Accord The 1996 Amendment The Basel II Accord The 1988 Basel Accord Risk Capital On-Balance Sheet Risk Charges Off-Balance Sheet Risk Charges Total Risk Charge Illustration The New Basel Accord Issues with the 1988 Basel Accord Definition of Capital The Credit Risk Charge The Operational Risk Charge Evaluation Conclusions Answers to Chapter Examples 707 Ch. 32 The Basel Market Risk Charges The Standardized Method The Internal Models Approach Qualitative Requirements The Market Risk Charge Combination of Approaches Stress Testing Backtesting Measuring Exceptions Statistical Decision Rules The Penalty Zones Answers to Chapter Examples 725 Index 729
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