Financial Risk Management: Models, History, and Institutions

Financial Risk
Management......Page 3
Contents......Page 9
List of Figures......Page 19
Preface......Page 23
1.1 Some History: Why Is Risk a Separate Discipline Today?......Page 29
1.1.1 The Financial Industry Since the 1960s......Page 30
1.1.2 The “Shadow Banking System”......Page 37
1.1.3 Changes in Public Policy Toward the Financial System......Page 43
1.1.4 The Rise of Large Capital Pools......Page 45
1.1.5 Macroeconomic Developments Since the 1960s: From the Unraveling of Bretton Woods to the Great Moderation......Page 48
1.2.1 Risk Management in Other Fields......Page 62
Further Reading......Page 69
CHAPTER 2 Market Risk Basics......Page 71
2.1 Arithmetic, Geometric, and Logarithmic Security Returns......Page 72
2.2 Risk and Securities Prices: The Standard Asset Pricing Model......Page 77
2.2.1 Defining Risk: States, Security Payoffs, and Preferences......Page 78
2.2.2 Optimal Portfolio Selection......Page 82
2.2.3 Equilibrium Asset Prices and Returns......Page 84
2.2.4 Risk-Neutral Probabilities......Page 89
2.3 The Standard Asset Distribution Model......Page 91
2.3.1 Random Walks and Wiener Processes......Page 92
2.3.2 Geometric Brownian Motion......Page 99
2.3.3 Asset Return Volatility......Page 102
2.4 Portfolio Risk in the Standard Model......Page 103
2.4.1 Beta and Market Risk......Page 104
2.4.2 Diversification......Page 110
2.4.3 Efficiency......Page 113
2.5 Benchmark Interest Rates......Page 116
Further Reading......Page 119
CHAPTER 3 Value-at-Risk......Page 121
3.1 Definition of Value-at-Risk......Page 122
3.1.1 The User-Defined Parameters......Page 125
3.1.2 Steps in Computing VaR......Page 126
3.2.1 Short-Term Conditional Volatility Estimation......Page 127
3.2.2 The EWMA Model......Page 132
3.2.3 The GARCH Model......Page 134
3.3.1 Parametric......Page 136
3.3.2 Monte Carlo Simulation......Page 137
3.3.3 Historical Simulation......Page 139
3.4 Short Positions......Page 141
3.5 Expected Shortfall......Page 142
Further Reading......Page 144
CHAPTER 4 Nonlinear Risks and the Treatment of Bonds and Options......Page 147
4.1 Nonlinear Risk Measurement and Options......Page 149
4.1.1 Nonlinearity and VaR......Page 151
4.1.2 Simulation for Nonlinear Exposures......Page 154
4.1.3 Delta-Gamma for Options......Page 155
4.1.4 The Delta-Gamma Approach for General Exposures......Page 162
4.2 Yield Curve Risk......Page 164
4.2.1 The Term Structure of Interest Rates......Page 166
4.2.2 Estimating Yield Curves......Page 169
4.2.3 Coupon Bonds......Page 172
4.3 VaR for Default-Free Fixed Income Securities Using The Duration and Convexity Mapping......Page 176
4.3.1 Duration......Page 177
4.3.2 Interest-Rate Volatility and Bond Price Volatility......Page 178
4.3.3 Duration-Only VaR......Page 180
4.3.4 Convexity......Page 182
4.3.5 VaR Using Duration and Convexity......Page 183
Further Reading......Page 184
CHAPTER 5 Portfolio VaR for Market Risk......Page 187
5.1 The Covariance and Correlation Matrices......Page 188
5.2 Mapping and Treatment of Bonds and Options......Page 190
5.3 Delta-Normal VaR......Page 191
5.3.1 The Delta-Normal Approach for a Single Position Exposed to a Single Risk Factor......Page 192
5.3.2 The Delta-Normal Approach for a Single Position Exposed to Several Risk Factors......Page 194
5.3.3 The Delta-Normal Approach for a Portfolio of Securities......Page 196
5.4 Portfolio VAR via Monte Carlo simulation......Page 202
5.5 Option Vega Risk......Page 203
5.5.1 Vega Risk and the Black-Scholes Anomalies......Page 204
5.5.2 The Option Implied Volatility Surface......Page 208
5.5.3 Measuring Vega Risk......Page 211
Further Reading......Page 218
CHAPTER 6 Credit and Counterparty Risk......Page 219
6.1 Defining Credit Risk......Page 220
6.2.1 The Economic Balance Sheet of the Firm......Page 221
6.2.2 Capital Structure......Page 222
6.2.3 Security, Collateral, and Priority......Page 223
6.3 Transaction Cost Problems in Credit Contracts......Page 224
6.4.1 Default......Page 227
6.4.2 Probability of Default......Page 228
6.4.4 Loss Given Default......Page 229
6.4.5 Expected Loss......Page 230
6.5.1 Credit Ratings and Rating Migration......Page 232
6.6 Counterparty Risk......Page 235
6.6.2 Measuring Counterparty Risk for Derivatives Positions......Page 237
6.6.4 Custodial Risk......Page 239
6.6.5 Mitigation of Counterparty Risk......Page 240
6.7 The Merton model......Page 241
6.8 Credit Factor Models......Page 250
6.9 Credit Risk Measures......Page 254
6.9.1 Expected and Unexpected Loss......Page 256
Further Reading......Page 257
7.1 Credit Spreads......Page 259
7.1.1 Spread Mark-to-Market......Page 261
7.2 Default Curve Analytics......Page 263
7.2.1 The Hazard Rate......Page 265
7.2.3 Default Time Density Function......Page 267
7.2.4 Conditional Default Probability......Page 268
7.3 Risk-Neutral Estimates of Default Probabilities......Page 269
7.3.1 Basic Analytics of Risk-Neutral Default Rates......Page 270
7.3.2 Time Scaling of Default Probabilities......Page 273
7.3.3 Credit Default Swaps......Page 274
7.3.4 Building Default Probability Curves......Page 278
7.3.5 The Slope of Default Probability Curves......Page 287
7.4.1 Mark-to-Market of a CDS......Page 289
7.4.2 Spread Volatility......Page 290
Further Reading......Page 292
CHAPTER 8 Portfolio Credit Risk......Page 293
8.1.1 Defining Default Correlation......Page 294
8.2.1 Granularity and Portfolio Credit Value-at-Risk......Page 298
8.3.1 Conditional Default Distributions......Page 303
8.3.2 Asset and Default Correlation......Page 307
8.3.3 Credit VaR Using the Single-Factor Model......Page 309
8.4 Using Simulation and Copulas to Estimate Portfolio Credit Risk......Page 312
8.4.1 Simulating Single-Credit Risk......Page 314
8.4.2 Simulating Joint Defaults with a Copula......Page 316
Further Reading......Page 323
9.1 Structured Credit Basics......Page 325
9.1.1 Capital Structure and Credit Losses in a Securitization......Page 329
9.1.2 Waterfall......Page 333
9.1.3 Issuance Process......Page 335
9.2.1 Tracking the Interim Cash Flows......Page 337
9.2.2 Tracking the Final-Year Cash Flows......Page 342
9.3.1 The Simulation Procedure and the Role of Correlation......Page 346
9.3.2 Means of the Distributions......Page 351
9.3.3 Distribution of Losses and Credit VaR......Page 355
9.3.4 Default Sensitivities of the Tranches......Page 361
9.3.5 Summary of Tranche Risks......Page 364
9.4 Standard Tranches and Implied Credit Correlation......Page 365
9.4.1 Credit Index Default Swaps and Standard Tranches......Page 366
9.4.2 Implied Correlation......Page 368
9.4.3 Summary of Default Correlation Concepts......Page 369
9.5 Issuer and Investor Motivations for Structured Credit......Page 370
9.5.1 Incentives of Issuers......Page 371
9.5.2 Incentives of Investors......Page 373
Further Reading......Page 374
10.1 Real-World Asset Price Behavior......Page 377
10.2.1 Jump-Diffusion Models......Page 391
10.2.2 Extreme Value Theory......Page 393
10.3.1 Option-Based Risk-Neutral Distributions......Page 400
10.3.2 Risk-Neutral Asset Price Probability Distributions......Page 408
10.3.3 Implied Correlations......Page 415
Further Reading......Page 418
11.1 Model Risk......Page 421
11.1.2 Variability of VaR Estimates......Page 423
11.1.3 Mapping Issues......Page 425
11.1.4 Case Study: The 2005 Credit Correlation Episode......Page 427
11.1.5 Case Study: Subprime Default Models......Page 433
11.2 Backtesting of VaR......Page 435
11.3 Coherence of VaR Estimates......Page 442
Further Reading......Page 447
CHAPTER 12 Liquidity and Leverage......Page 449
12.1.1 Maturity Transformation......Page 450
12.1.2 Liquidity Transformation......Page 451
12.1.3 Bank Liquidity......Page 453
12.1.4 Structured Credit and Off-Balance-Sheet Funding......Page 457
12.1.5 Funding Liquidity of Other Intermediaries......Page 460
12.1.6 Systematic Funding Liquidity Risk......Page 462
12.2 Markets for Collateral......Page 465
12.2.1 Structure of Markets for Collateral......Page 466
12.2.2 Economic Function of Markets for Collateral......Page 469
12.2.3 Prime Brokerage and Hedge Funds......Page 471
12.2.4 Risks in Markets for Collateral......Page 473
12.3.1 Defining and Measuring Leverage......Page 476
12.3.2 Margin Loans and Leverage......Page 482
12.3.3 Short Positions......Page 483
12.3.4 Derivatives......Page 484
12.3.6 Asset Volatility and Leverage......Page 488
12.4.1 Causes of Transactions Liquidity Risk......Page 489
12.4.2 Characteristics of Market Liquidity......Page 491
12.5.1 Measuring Funding Liquidity Risk......Page 492
12.5.2 Measuring Transactions Liquidity Risk......Page 494
12.6.1 Funding Liquidity and Solvency......Page 497
12.6.3 Systemic Risk and the “Plumbing”......Page 499
12.6.4 “Interconnectedness”......Page 501
Further Reading......Page 502
CHAPTER 13 Risk Control and Mitigation......Page 505
13.1 Defining Risk Capital......Page 506
13.2 Risk Contributions......Page 508
13.2.1 Risk Contributions in a Long-Only Portfolio......Page 509
13.2.2 Risk Contributions Using Delta Equivalents......Page 513
13.2.3 Risk Capital Measurement for Quantitative Strategies......Page 518
13.3 Stress Testing......Page 527
13.3.1 An Example of Stress Testing......Page 529
13.3.2 Types of Stress Tests......Page 532
13.4.1 Diversification......Page 534
13.4.2 Optimization and Implied Views......Page 535
13.5 Risk Reporting......Page 537
13.6 Hedging and Basis Risk......Page 540
Further Reading......Page 544
CHAPTER 14 Financial Crises......Page 545
14.1.1 Monetary and Credit Contraction......Page 547
14.1.2 Panics......Page 556
14.1.3 Rising Insolvencies......Page 563
14.1.4 Impairment of Market Functioning......Page 565
14.2 Self-Reinforcing Mechanisms......Page 567
14.2.1 Net Worth and Asset Price Declines......Page 568
14.2.2 Collateral Devaluation......Page 570
14.2.3 Risk Triggers......Page 571
14.2.4 Accounting Triggers......Page 575
14.3 Behavior of Asset Prices During Crises......Page 576
14.3.1 Credit Spreads......Page 577
14.3.2 Extreme Volatility......Page 579
14.3.3 Correlations......Page 584
14.4 Causes of Financial Crises......Page 590
14.4.1 Debt, International Payments, and Crises......Page 591
14.4.2 Interest Rates and Credit Expansion......Page 598
14.4.3 Procyclicality: Financial Causes of Crises......Page 603
14.4.4 Models of Bubbles and Crashes......Page 606
14.5.1 Identifying Financial Fragility......Page 611
14.5.3 Asset-Price Predictors of Financial Crises......Page 613
Further Reading......Page 619
CHAPTER 15 Financial Regulation......Page 625
15.1.1 The Rationale of Regulation......Page 626
15.1.2 Regulatory Authorities......Page 629
15.2 Methods of Regulation......Page 633
15.2.1 Deposit Insurance......Page 634
15.2.2 Capital Standards......Page 636
15.2.3 Bank Examinations and Resolution......Page 647
15.3.1 Financial Stability Policies......Page 649
15.3.2 Lender of Last Resort......Page 656
15.4 Pitfalls in Regulation......Page 663
15.4.1 Moral Hazard and Risk Shifting......Page 664
15.4.2 Regulatory Evasion......Page 671
15.4.3 Unintended Consequences......Page 673
Further Reading......Page 675
A.1 Binomial Distribution......Page 681
A.2 Quantiles and Quantile Transformations......Page 682
A.3.1 Relationship between Asset Price Levels and Returns......Page 684
A.3.2 The Black-Scholes Distribution Function......Page 685
A.4 Hypothesis Testing......Page 689
A.5 Monte Carlo Simulation......Page 690
A.5.1 Fooled by Nonrandomness: Random Variable Generation......Page 691
A.6 Homogeneous Functions......Page 692
Further Reading......Page 694
APPENDIX B Abbreviations......Page 695
APPENDIX C References......Page 699
Index......Page 729