Financial Risk Manager Handbook

Preface; Introduction; Part I: Quantitative Analysis; Ch. 1: Bond Fundamentals; 1.1 Discounting, Present, and Future Value; 1.2 Price-Yield Relationship; 1.2.1 Valuation; 1.2.2 Taylor Expansion; 1.2.3 Bond Price Derivatives; 1.2.4 Interpreting Duration and Convexity; 1.2.5 Portfolio Duration and Convexity; 1.3 Answers to Chapter Examples; Ch. 2: Fundamentals of Probability; 2.1 Characterizing Random Variables; 2.1.1 Univariate Distribution Functions; 2.1.2 Moments; 2.2 Multivariate Distribution Functions; 2.3 Functions of Random Variables; 2.3.1 Linear Transformation of Random Variables; 2.3.2 Sum of Random Variables; 2.3.3 Portfolios of Random Variables; 2.3.4 Product of Random Variables; 2.3.5 Distributions of Transformations of Random Variables; 2.4 Important Distribution Functions; 2.4.1 Uniform Distribution; 2.4.2 Normal Distribut ion; 2.4.3 Lognormal Distribution; 2.4.4 Student's Distribution; 2.4.5 Binomial Distribution; 2.5 Answers to Chapter Examples; Ch. 3: Fundamentals of Statistics; 3.1 Real Data; 3.1.1 Measuring Returns; 3.1.2 Time Aggregation; 3.1.3 Portfolio Aggregation; 3.2 Parameter Estimation; 3.3 Regression Analysis; 3.3.1 Bivariate Regression; 3.3.2 Autoregression; 3.3.3 Multivariate Regression; 3.3.4 Example; 3.3.5 Pitfalls with Regressions; 3.4 Answers to Chapter Examples; Ch. 4: Monte Carlo Methods; 4.1 Simulations with One Random Variable; 4.1.1 Simulating Markov Processes; 4.1.2 The Geometric Brownian Motion; 4.1.3 Simulating Yields; 4.1.4 Binomial Trees; 4.2 Implementing Simulations; 4.2.1 Simulation for VAR; 4.2.2 Simulation for Derivatives; 4.2.3 Accuracy; 4.3 Multiple Sources of Risk; 4.3.1 The Cholesky Factorization; 4.4 Answers to Chapter Examples; Part II: Capital Markets; Ch. 5: Introduction to Derivatives; 5.1 Overview of Derivatives Markets; 5.2 Forward Contracts; 5.2.1 Definition; 5.2.2 Valuing Forward Contracts; 5.2.3 Valuing an Off-Market Forward Contract; 5.2.4 Valuing Forward Contracts with Income Payments; 5.3 Futures Contracts; 5.3.1 Definitions of Futures; 5.3.2 Valuing Futures Contracts; 5.4 Swap Contracts; 5.5 Answers to Chapter Examples; Ch. 6: Options; 6.1 Option Payoffs; 6.1.1 Basic Options; 6.1.2 Put-Call Parity; 6.1.3 Combination of Options; 6.2 Valuing Options; 6.2.1 Option Premiums; 6.2.2 Early Exercise of Options; 6.2.3 Black-Scholes Valuation; 6.2.4 Market vs. Model Prices; 6.3 Other Option Contracts; 6.4 Valuing Options by Numerical Methods; 6.5 Answers to Chapter Examples; Ch. 7: Fixed-Income Securities; 7.1 Overview of Debt Markets; 7.2 Fixed-Income Securities; 7.2.1 Instrument Types; 7.2.2 Methods of Quotation; 7.3 Analysis of Fixed-Income Securities; 7.3.1 The NPV Approach; 7.3.2 Duration; 7.4 Spot and Forward Rates; 7.5 Mortgage-Backed Securities; 7.5.1 Description; 7.5.2 Prepayment Risk; 7.5.3 Financial Engineering and CMOs; 7.6 Answers to Chapter Examples; Ch. 8: Fixed-Income Derivatives; 8.1 Forward Contracts; 8.2 Futures; 8.2.1 Eurodollar Futures; 8.2.2 T-bond Futures; 8.3 Swaps; 8.3.1 Definitions; 8.3.2 Quotations; 8.3.3 Pricing; 8.4 Options; 8.4.1 Caps and Floors; 8.4.2 Swaptions; 8.4.3 Exchange-Traded Options; 8.5 Answers to Chapter Examples; Ch. 9: Equity Markets; 9.1 Equities; 9.1.1 Overview; 9.1.2 Valuation; 9.1.3 Equity Indices; 9.2 Convertible Bonds and Warrants; 9.2.1 Definitions; 9.2.2 Valuation; 9.3 Equity Derivatives; 9.3.1 Stock Index Futures; 9.3.2 Single Stock Futures; 9.3.3 Equity Options; 9.3.4 Equity Swaps; 9.4 Answers to Chapter Examples; Ch. 10: Currencies and Commodities Markets; 10.1 Currency Markets; 10.2 Currency Swaps; 10.2.1 Definitions; 10.2.2 Pricing; 10.3 Commodities; 10.3.1 Products; 10.3.2 Pricing of Futures; 10.3.3 Futures and Expected Spot Prices; 10.4 Answers to Chapter Examples; Part III: Market Risk Management; Ch. 11: Introduction to Market Risk Measurement; 11.1 Introduction to Financial Market Risks; 11.2 VAR as Downside Risk; 11.2.1 VAR: Definition; 11.2.2 VAR: Caveats; 11.2.3 Alternative Measures of Risk; 11.3 VAR: Parameters; 11.3.1 Confidence Level; 11.3.2 Horizon; 11.3.3 Application: The Basel Rules; 11.4 Elements of VAR Systems; 11.4.1 Portfolio Positions; 11.4.2 Risk Factors; 11.4.3 VAR Methods; 11.5 Stress-Testing; 11.6 Cash Flow at Risk; 11.7 Answers to Chapter Examples; Ch. 12: Identification of Risk Factors; 12.1 Market Risks; 12.1.1 Absolute and Relative Risk; 12.1.2 Directional and Nondirectional Risk; 12.1.3 Market vs. Credit Risk; 12.1.4 Risk Interaction; 12.2 Sources of Loss: A Decomposition; 12.2.1 Exposure and Uncertainty; 12.2.2 Specific Risk; 12.3 Discontinuity and Event Risk; 12.3.1 Continuous Processes; 12.3.2 Jump Process; 12.3.3 Event Risk; 12.4 Liquidity Risk; 12.5 Answers to Chapter Examples; Ch. 13: Sources of Risk; 13.1 Currency Risk; 13.1.1 Currency Volatility; 13.1.2 Correlations; 13.1.3 Devaluation Risk; 13.1.4 Cross-Rate Volatility; 13.2 Fixed-Income Risk; 13.2.1 Factors Affecting Yields; 13.2.2 Bond Price and Yield Volatility; 13.2.3 Correlations; 13.2.4 Global Interest Rate Risk; 13.2.5 Real Yield Risk; 13.2.6 Credit Spread Risk; 13.2.7 Prepayment Risk; 13.3 Equity Risk; 13.3.1 Stock Market Volatility; 13.3.2 Forwards and Futures; 13.4 Commodity Risk; 13.4.1 Commodity Volatility Risk; 13.4.2 Forwards and Futures; 13.4.3 Delivery and Liquidity Risk; 13.5 Risk Simplification; 13.5.1 Diagonal Model; 13.5.2 Factor Models; 13.5.3 Fixed-Income Portfolio Risk; 13.6 Answers to Chapter Examples; Ch. 14: Hedging Linear Risk; 14.1 Introduction to Futures Hedging; 14.1.1 Unitary Hedging; 14.1.2 Basis Risk; 14.2 Optimal Hedging; 14.2.1 The Optimal Hedge Ratio; 14.2.2 The Hedge Ratio as Regression Coefficient; 14.2.3 Example; 14.2.4 Liquidity Issues; 14.3 Applications of Optimal Hedging; 14.3.1 Duration Hedging; 14.3.2 Beta Hedging; 14.4 Answers to Chapter Examples; Ch. 15: Nonlinear Risk: Options; 15.1 Evaluating Options; 15.1.1 Definitions; 15.1.2 Taylor Expansion; 15.1.3 Option Pricing; 15.2 Option "Greeks"; 15.2.1 Option Sensitivities: Delta and Gamma; 15.2.2 Option Sensitivities: Vega; 15.2.3 Option Sensitivities: Rho; 15.2.4 Option Sensitivities: Theta; 15.2.5 Option Pricing and the "Greeks"; 15.2.6 Option Sensitivities: Summary; 15.3 Dynamic Hedging; 15.3.1 Delta and Dynamic Hedging; 15.3.2 Implications; 15.3.3 Distribution of Option Payoffs; 15.4 Answers to Chapter Examples; Ch. 16: Modeling Risk Factors; 16.1 The Normal Distribution; 16.1.1 Why the Normal?; 16.1.2 Computing Returns; 16.1.3 Time Aggregation; 16.2 Fat Tails; 16.3 Time-Variation in Risk; 16.3.1 GARCH; 16.3.2 EWMA; 16.3.3 Option Data; 16.3.4 Implied Distributions; 16.4 Answers to Chapter Examples; Ch. 17: VAR Methods; 17.1 VAR: Local vs. Full Valuation; 17.1.1 Local Valuation; 17.1.2 Full Valuation; 17.1.3 Delta-Gamma Method; 17.2 VAR Methods: Overview; 17.2.1 Mapping; 17.2.2 Delta-Normal Method; 17.2.3 Historical Simulation Method; 17.2.4 Monte Carlo Simulation Method; 17.2.5 Comparison of Methods; 17.3 Example; 17.3.1 Mark-to-Market; 17.3.2 Risk Factors; 17.3.3 VAR: Historical Simulation; 17.3.4 VAR: Delta-Normal Method; 17.4 Risk Budgeting; 17.5 Answers to Chapter Examples; Part IV: Credit Risk Management; Ch. 18: Introduction to Credit Risk; 18.1 Settlement Risk; 18.1.1 Presettlement vs. Settlement Risk; 18.1.2 Handling Settlement Risk; 18.2 Overview of Credit Risk; 18.2.1 Drivers of Credit Risk; 18.2.2 Measurement of Credit Risk; 18.2.3 Credit Risk vs. Market Risk; 18.3 Measuring Credit Risk; 18.3.1 Credit Losses; 18.3.2 Joint Events; 18.3.3 An Example; 18.4 Credit Risk Diversification; 18.5 Answers to Chapter Examples; Ch. 19: Measuring Actuarial Default Risk; 19.1 Credit Event... 412; 19.2 Default Rates; 19.2.1 Credit Ratings; 19.2.2 Historical Default Rates; 19.2.3 Cumulative and Marginal Default Rates; 19.2.4 Transition Probabilities; 19.2.5 Predicting Default Probabilities; 19.3 Recovery Rates; 19.3.1 The Bankruptcy Process; 19.3.2 Estimates of Recovery Rates; 19.4 Application to Portfolio Rating; 19.5 Assessing Corporate and Sovereign Rating; 19.5.1 Corporate Default; 19.5.2 Sovereign Default; 19.6 Answers to Chapter Examples; Ch. 20: Measuring Default Risk from Market Prices; 20.1 Corporate Bond Prices; 20.1.1 Spreads and Default Risk; 20.1.2 Risk Premium; 20.1.3 The Cross-Section of Yield Spreads; 20.1.4 The Time-Series of Yield Spreads; 20.2 Equity Prices; 20.2.1 The Merton Model; 20.2.2 Pricing Equity and Debt; 20.2.3 Applying the Merton Model; 20.2.4 Example; 20.3 Answers to Chapter Examples; Ch. 21: Credit Exposure; 21.1 Credit Exposure by Instrument; 21.2 Distribution of Credit Exposure; 21.2.1 Expected and Worst Exposure; 21.2.2 Time Profile; 21.2.3 Exposure Profile for Interest-Rate Swaps; 21.2.4 Exposure Profile for Currency Swaps; 21.2.5 Exposure Profile for Different Coupons; 21.3 Exposure Modifiers; 21.3.1 Marking to Market; 21.3.2 Exposure Limits; 21.3.3 Recouponing; 21.3.4 Netting Arrangements; 21.4 Credit Risk Modifiers; 21.4.1 Credit Triggers; 21.4.2 Time Puts; 21.5 Answers to Chapter Examples; Ch. 22: Credit Derivatives; 22.1 Introduction; 22.2 Types of Credit Derivatives; 22.2.1 Credit Default Swaps; 22.2.2 Total Return Swaps; 22.2.3 Credit Spread Forward and Options; 22.2.4 Credit-Linked Notes; 22.3 Pricing and Hedging Credit Derivatives; 22.3.1 Methods; 22.3.2 Example: Credit Default Swap; 22.4 Pros and Cons of Credit Derivatives; 22.5 Answers to Chapter Examples; Ch. 23: Managing Credit Risk; 23.1 Measuring the Distribution of Credit Losses; 23.2 Measuring Expected Credit Loss; 23.2.1 Expected Loss over a Target Horizon; 23.2.2 The Time Profile of Expected Loss; 23.3 Measuring Credit VAR; 23.4 Portfolio Credit Risk Models; 23.4.1 Approaches to Portfolio Credit Risk Models; 23.4.2 CreditMetrics; 23.4.3 CreditRisk+; 23.4.4 Moody's KMV; 23.4.5 Credit Portfolio View; 23.4.6 Comparison; 23.5 Answers to Chapter Examples; Part V: Operational and Integrated Risk Management; Ch. 24: Operational Risk; 24.1 The Importance of Operational Risk; 24.1.1 Case Histories; 24.1.2 Business Lines; 24.2 Identifying Operational Risk; 24.3 Assessing Operational Risk; 24.3.1 Comparison of Approaches; 24.3.2 Acturial Models; 24.4 Managing Operational Risk; 24.4.1 Capital Allocation and Insurance; 24.4.2 Mitigating Operational Risk; 24.5 Conceptual Issues; 24.6 Answers to Chapter Examples; Ch. 25: Risk Capital and RAROC; 25.1 RAROC; 25.1.1 Risk Capital; 25.1.2 RAROC Methodology; 25.1.3 Application to Compensation; 25.2 Performance Evaluation and Pricing; 25.3 Answers to Chapter Examples; Ch. 26: Best Practices Reports; 26.1 The G-30 Report; 26.2 The Bank of England Report on Barings; 26.3 The CRMPG Report on LTCM; 26.4 Answers to Chapter Examples; Ch. 27: Firmwide Risk Management; 27.1 Types of Risk; 27.2 Three-Pillar Framework; 27.2.1 Best-Practice Policies; 27.2.2 Best-Practice Methodologies; 27.2.3 Best-Practice Infrastructure; 27.3 Organizational Structure; 27.4 Controlling Traders; 27.4.1 Trader Compensation; 27.4.2 Trader Limits; 27.5 Answers to Chapter Examples; Part VI: Legal, Accounting, and Tax Risk Management; Ch. 28: Legal Issues; 28.1 Legal Risks with Derivatives; 28.2 Netting; 28.2.1 G-30 Recommendations; 28.2.2 Netting under the Basel Accord; 28.2.3 Walk-Away Clauses; 28.2.4 Netting and Exchange Margins; 28.3 ISDA Master Netting Agreement; 28.4 The 2002 Sarbanes-Oxley Act; 28.5 Glossary; 28.5.1 General Legal Terms; 28.5.2 Bankruptcy Terms; 28.5.3 Contract Terms; 28.6 Answers to Chapter Examples; Ch. 29: Accounting and Tax Issues; 29.1 Internal Reporting; 29.1.1 Purpose of Internal Reporting; 29.1.2 Comparison of Methods; 29.1.3 Historical Cost versus Marking-to-Market; 29.2 External Reporting: FASB; 29.2.1 FAS 133; 29.2.2 Definition of Derivative; 29.2.3 Embedded Derivative; 29.2.4 Disclosure Rules; 29.2.5 Hedge Effectiveness; 29.2.6 General Evaluation of FAS 133; 29.2.7 Accounting Treatment of SPEs; 29.3 External Reporting: IASB; 29.3.1 IAS 37; 29.3.2 IAS 39; 29.4 Tax Considerations; 29.5 Answers to Chapter Examples; Part VII: Regulation and Compliance; Ch. 30: Regulation of Financial Institutions; 30.1 Definition of Financial Institutions; 30.2 Systemic Risk; 30.3 Regulation of Commercial Banks; 30.4 Regulation of Securities Houses; 30.5 Tools and Objectives of Regulation; 30.6 Answers to Chapter Examples; Ch. 31: The Basel Accord; 31.1 Steps in The Basel Accord; 31.1.1 The 1988 Accord; 31.1.2 The 1996 Amendment; 31.1.3 The New Basel Accord; 31.2 The 1988 Basel Accord; 31.2.1 Risk Capital; 31.2.2 On-Balance-Sheet Risk Charges; 31.2.3 Off-Balance-Sheet Risk Charges; 31.2.4 Total Risk Charge; 31.3 Illustration; 31.4 The New Basel Accord; 31.4.1 Issues with the 1988 Basel Accord; 31.4.2 The New Basel Accord: Credit Risk Charges; 31.4.3 Securitization and Credit Risk Mitigation; 31.4.4 The Basel Operational Risk Charge; 31.5 Answers to Chapter Examples; 31.6 Further Information; Ch. 32: The Basel Market Risk Charges; 32.1 The Standardized Method; 32.2 The Internal Models Approach; 32.2.1 Qualitative Requirements; 32.2.2 The Market Risk Charge; 32.2.3 Combination of Approaches; 32.3 Stress-Testing; 32.4 Backtesting; 32.4.1 Measuring Exceptions; 32.4.2 Statistical Decision Rules; 32.4.3 The Penalty Zones; 32.5 Answers to Chapter Examples; Index