Preface xi

Acknowledgments xvii

**CHAPTER 1 Introduction 1**

Banks and Risk Management 1

Evolution of Bank Capital Regulation 4

Creating Value from Risk Management 9

Financial Risk Systems 10

Risk Analytics 11

Risk Infrastructure 13

Risk Technology 15

Model Risk Management 17

**PART ONE ****Market Risk**

**CHAPTER 2 Market Risk with the Normal Distribution 23**

Linear Portfolios 24

Basic Model 24

Risk Measures 28

Risk Contributions 31

Estimating the Covariance Matrix of Risk Factors 39

Distribution of Risk Measures 40

Probabilistic Stress Testing 41

Quadratic Portfolios 43

Quadratic Portfolio Representation 44

Quadratic Portfolio Distribution 50

Calculation of Risk Measures for the Quadratic Portfolio 51

Simulation-Based Valuation 53

Example of Barrier Stock Options and Position Nonlinearity 54

Simulation from the Multivariate Normal Distribution 56

Risk Factor Dimension Reduction 60

Incorporating Model Estimation Error in the Simulation Scheme 65

Variance Reduction by Importance Sampling 66

Reducing Pricing Time 69

**CHAPTER 3 Advanced Market Risk Analysis 75**

Risk Measures, Risk Contributions, and Risk Information 75

VaR Interval Estimation 76

Coherent Measures of Risk 79

Simulation-Based Risk Contributions 80

Risk Information Measures 88

Risk Distortion Measures 93

Modeling the Stylized Facts of Financial Time Series 97

Univariate Time Series 97

Multivariate Time Series 110

Model Validation and Backtesting 122

A Multivariate Model of Risk Factor Returns 127

Time Scaling VaR and VaR with Trading 134

Time Aggregation of VaR with Constant Portfolios 134

Time Aggregation of VaR with Trading 135

Market Liquidity Risk 136

Closeout Time with No Liquidity Cost 137

A Note on General Market Illiquidity Models 140

Scenario Analysis and Stress Testing 142

Portfolio Sensitivity Analysis 143

Systematic Portfolio Stress Tests 143

Hypothetical Scenario from Reverse Stress Testing 147

Integration of Stress and Model Analysis 154

Portfolio Optimization 155

Portfolio Mean Risk Optimization 156

Cash Flow Replication 161

Developments in the Market Risk Internal Models Capital Regulation 165

**PART TWO ****Credit Risk**

**CHAPTER 4 Portfolio Credit Risk 171**

Issuer Credit Risk in Wholesale Exposures and Trading Book 174

Market Pricing of Corporate Bonds 174

Merton’s Structural Model for Corporate Bond Pricing 178

The Multivariate Merton Model 185

Applied Portfolio Migration and Default Risk Models 187

Economic Capital for a Portfolio of Traded Bonds 230

Credit Models for the Banking Book 235

The Binomial Loss Model 236

Credit Transition Score Models 242

Simulation of State Transitions and Markov Iteration 254

Mortgage Portfolio Risk Analysis: An Illustration 258

Point in Time and Through the Cycle Models—with Applications to Regulatory Stress Testing 277

An Economic Capital Model for Loan Portfolios 285

The Poisson Mixture Model and CreditRisk^{+} 289

Firmwide Portfolio Credit Risk and Credit Risk Dependence 296

Joint Codependency with Different Models 297

Indirect and Direct Codependency in Credit Risk Models 298

Credit Risk Stress Testing 299

Stress Testing with Multifactor Model 301

Stress Testing with Macroeconomic Credit Score Model 303

Features of New Generation Portfolio Credit Risk Models 309

Multi-Horizon Models for Banking Book 309

Modeling the Recovery Process for Banking Book Portfolios 310

Earnings and Loss Rather than Just Loss 311

Loan-Level Models 314

Granularity of Credit Factors 314

Hedging Credit Risk 315

Single-Name Credit Default Swaps 315

Credit Default Swaps on Portfolio Indices 320

Basket Credit Default Swaps 321

Regulatory Capital for Credit Risk 324

Regulatory Risk Components 326

Risk Mitigation and Regulatory Capital 327

Appendix 328

**CHAPTER 5 Counterparty Credit Risk 333**

Counterparty Pricing and Exposure 335

Market Standard Pricing Metrics 335

Assessment of Counterparty Default Probability 343

Exposure Simulation Framework for CVA 346

Market Correlations, Wrong-Way Risk, and Counterparty Pricing 360

Collateralized Exposures 364

CVA Risks 382

Portfolios of Derivatives 384

Netting 384

Marginal and Incremental Portfolio Trades 386

Recent Counterparty Credit Risk Developments 392

OIS Discounting for Derivatives 392

Advanced CVA Calculations and CVA Greeks 393

Funding Value Adjustments 394

Counterparty Credit Risk Regulation 395

Basel Counterparty Default Risk Charges 395

Enhanced Requirements on Counterparty Default Risk Charges 396

New Basel III Capital Requirements for Counterparty Credit Risk 397

Mitigating Regulatory Costs 399

**PART THREE ****Asset and Liability Management**

**CHAPTER 6 Liquidity Risk Management with Cash Flow Models 403**

Measurement of Liquidity Risk 407

Liquidity Exposure with General Liquidity Hedging Capacity 408

Liquidity Exposure with Cash Hedging Capacity 411

Components of the Liquidity Measure 412

Liquidity Exposure 414

Balance Sheet Cash Flows and Facilities 417

Off–Balance-Sheet Derivative Flows 427

Combining the Risk and Finance View 428

Hedging the Liquidity Exposure 428

Ranking-Based Liquidity Hedging Strategy 432

Optimal Liquidity Hedging Strategy 433

Structural Liquidity Planning 441

Mitigating Balance Sheet Vulnerability with Contractual Cash Flows 442

Choosing the Optimal Liquidity Hedging Portfolio 445

Components of the Liquidity Hedging Program 449

Cash Liquidity Risk and Liquidity Risk Measures 450

Cash Liquidity at Risk 450

Portfolio Cash Liquidity Exposure 451

Allocating Cash Liquidity Risk 453

Regulation for Liquidity Risk 455

Liquidity Coverage Ratio 455

Net Stable Funding Ratio 458

Regulatory Liquidity Monitoring Tools 459

**CHAPTER 7 Funds Transfer Pricing and Profitability of Cash Flows 463**

Basic Funds Transfer Pricing Concept 465

Example of FTP for a Mortgage and a Loan 466

Risk-Based Funds Transfer Pricing 468

Credit Risk and Capital 468

Embedded Optionality 470

Liquidity Risk 477

Funds Transfer Rate and Risk Adjusted Returns 481

Example of Mortgage Risk Adjusted Returns 481

Profitability Measures and Decompositions 482

Balance Sheet Breakdown with Funds Transfer Instruments 482

Application to Net Interest Income and Economic Value View 483

Banking Book Fair Value with Funds Transfer Rates 486

Example of Fair Values with FTP 486

A Note on the Scope of Funds Transfer Pricing 486

Regulation and Profitability Analysis 487

**PART FOUR ****Firmwide Risk**

**CHAPTER 8 Firmwide Risk Aggregation 493**

Correlated Aggregation and Firmwide Risk Levels 494

Linear Risk Aggregation 495

Copula Aggregation 497

Example of Copula Aggregation 497

Mixed Copula Aggregation 498

Example of Mixed Copula Aggregation 499

Capital Allocation in Risk Aggregation 501

Example of Mixed Copula Capital Allocation 502

Measuring Concentration and Diversification 503

Risk Aggregation and Regulation 503

**CHAPTER 9 Firmwide Scenario Analysis and Stress Testing 507**

Firmwide Scenario Model Approaches 509

Silo Approach 509

Firmwide Risk Model Approach 510

Multiple Model Approaches 512

Firmwide Risk Capital Measures 512

Risk Measures and Stress Scenarios 512

A Risk Reserve Approach—A Practical Illustration 514

Regulatory Stress Scenario Approach 516

Bank-Specific Approach: A Total Balance Sheet View 517

Bank-Specific Approach: More on Scenarios and Models 520

Systemic View: Financial System Analysis and Financial Contagion 523

The Future of Firmwide Stress Testing 524

References 527

Index 543