Financial Risk Manager Handbook
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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.
