About the Author xvii
Preface xix
Abbreviations xxiii
Introduction 1
Asset-Liability Management Metrics 5
ALM Risk Factors 7
Organization of This Book 8
Chapter 1 Interest Rate 17
Interest Rate, Future Value, and Compounding 18
Use of Time Notation versus Period Notation 22
Simple Interest 23
Accrual and Payment Periods 24
Present Value and Discount Factor 29
Present Value of Several Cash Flows 32
Present Value of Annuity and Perpetuity 33
Day Count and Business Day Conventions 34
Treasury Yield Curve and Zero-Coupon Rate 40
Bootstrapping 43
LIBOR 48
Forward Rates and Future Rates 49
Implied Forward Rates 50
Forward Rate Agreements 55
Interest Rate Futures 56
Swap Rate 58
Determination of the Swap Rate 61
Valuation of Interest Rate Swap Contracts 66
LIBOR-Swap Spot Curve 70
Interpolation Methods 75
Piecewise Linear Interpolation 76
Piecewise Cubic Spline Interpolation 78
Federal Funds and Prime Rates 84
Overnight Index Swap Rate 87
OIS Discounting 88
Secured Overnight Financing Rate 94
Components of Interest Rate 95
Risk Structure of Interest Rate 97
Term Structure of Interest Rate 98
Expectation Theory 100
Market Segmentation Theory 102
Liquidity Premium Theory 102
Inflation and Interest Rate 102
Negative Interest Rate 103
Interest Rate Shock 105
Parallel Shock 106
Non-Parallel Shock 107
Interest Rate Risk 109
Summary 110
Notes 112
Bibliography 114
Chapter 2 Valuation: Fundamentals of Fixed-Income and Non-Maturing Products 115
Principal Amortization 116
Bullet Payment at Maturity 116
Linear Amortization 117
Constant Payment Amortization 118
Sum-of-Digits Amortization 121
Custom Amortization Schedule 123
Fixed-Rate Instrument 124
Valuation 124
Yield 130
Duration and Convexity 133
Dollar Duration and Dollar Convexity 142
Portfolio Duration and Convexity 143
Effective Duration and Effective Convexity 144
Interest Rate Risk Immunization 145
Key Rate Duration 155
Fisher-Weil Duration 156
Key Rate Duration 160
Floating-Rate Instrument 165
Pre-Period-Initiation Rate Setting 166
Post-Period-Initiation Rate Setting 166
Valuation Using Estimated Interest Rates at Future Reset Dates 168
Using Implied Forward Rate 168
Using Forecasted Rate 171
Valuation Using Assumption of Par Value at Next Reset Date 177
Duration and Convexity 182
Valuation Using Simulated Interest Rate Paths 184
Non-Maturing Instrument 191
No New Business Treatment 192
No New Account Treatment 196
Constant Balance Treatment 197
Inclusion of Prepayment and Default: A Roll Forward Approach 198
Summary 207
Notes 210
Bibliography 210
Chapter 3 Equity Valuation 213
Dividend Discount Model 214
Discounted Free Cash Flow Method 217
Comparative Valuation Using Price Ratios 226
Summary 233
Note 234
Bibliography 235
Chapter 4 Option Valuation 237
Stock Option 238
Boundary Values 240
Call Option 241
Put Option 243
Put-Call Parity 247
Underlying Stock Does Not Pay Dividends 247
Underlying Stock Pays Dividends or Provides Yield 251
Binomial Tree 252
The Black-Scholes-Merton Model 267
Generalization of the Black-Scholes-Merton Model 272
Option Valuation Using Monte Carlo Simulation 273
Sensitivity of Option Value 282
Sensitivity to Underlying Price 282
Sensitivity to Volatility 288
Sensitivity to the Interest Rate 290
Sensitivity to the Passage of Time 291
Volatility 292
Historical Volatility 292
Implied Volatility 295
Non-Constant Volatility 297
ARCH and GARCH Models 298
Forecasting Volatility Using the GARCH Model 303
The GARCH-M Model 305
The Exponentially Weighted Moving Average Model 306
The EWMA Model for Covariance 310
Option Valuation Using a GARCH Model 312
Futures Options 319
Futures Contract 319
Option on Futures Contract 320
Put-Call Parity for Futures Options 323
Black Model 324
Using a Binomial Tree for Valuation of Futures Options 326
Summary 328
Annex 1: Derivation of Put-Call Parity When the Underlying Pays Dividends 331
Annex 2: Derivation of Delta, Gamma, Vega, Rho, and Theta 338
Notes 343
Bibliography 344
Chapter 5 Interest Rate Models 347
Instantaneous Forward Rate and Short Rate 347
Vasicek Model 354
Hull-White Model 358
Ho-Lee Model 366
Black-Karasinski Model 367
Interest Rate Options 368
Swaption 368
Interest Rate Cap and Floor 370
Analytical Valuation of Bonds and Options 373
Zero-Coupon Bond 373
Option on a Zero-Coupon Bond 374
Interest Rate Cap and Floor 375
Option on a Coupon-Bearing Bond 376
Swaption 376
Interest Rate Tree 377
The Hull-White Tree 382
The Black-Karasinski Tree 400
Calibration 405
Calibration Using the Analytical Method 408
Calibration Using the Interest Rate Tree 413
LIBOR Market Model 420
Summary 425
Annex: Derivation of Zero-Coupon Bond Price Using a t-Period Rate from the Hull-White Tree 427
Notes 429
Bibliography 430
Chapter 6 Valuation of Bonds with Embedded Options 433
Callable Bond 433
Option-Adjusted Spread 441
Putable Bond 444
Summary 446
Note 447
Bibliography 447
Chapter 7 Valuation of Mortgage-Backed and Asset-Backed Securities 449
Mortgage-Backed Securities 450
Fixed-Rate Conventional Mortgage Loans 452
Prepayment 460
Impact of Prepayment on Mortgage-Backed Securities 463
Valuation of Mortgage-Backed Securities 476
Short Rate Model 476
Mortgage Refinancing Rate Model 480
Prepayment Model 483
Cash Flow Generator 483
Discounting and Aggregation Platform 484
Number of Simulated Paths and Convergence 486
Impact of Default on Mortgage-Backed Securities 488
Collateralized Mortgage Obligations 503
Valuation of Collateralized Mortgage Obligations 511
Asset-Backed Securities 513
Auto Loan ABSs 517
Collateral 517
Structure 520
Prepayment 521
Home Equity Loan ABSs 522
Collateral 522
Structure 523
Prepayment 524
Student Loan ABSs 524
Collateral 524
Structure 528
Prepayment 529
Credit Card Receivable ABSs 529
Collateral 529
Structure 530
Cash Flow Distribution Method 531
Prepayment 534
Early Amortization Event 534
Valuation of Asset-Backed Securities 535
Summary 550
Annex: Derivation of Survival Factor 552
Notes 553
Bibliography 554
Chapter 8 Economic Value of Equity 557
Economic Value of Equity: Basics 559
Duration Gap 562
Risk-Adjusted Yield Curve 567
Interest Rate Scenario Analysis 574
Product Type and Value Sensitivity 575
Impact of Interest Rate Shocks on EVE 584
Balance Sheet Type and EVE Sensitivity 593
Currency Exchange Rate Scenario Analysis 594
Economic Value of Equity Risk Limits 597
Balance Sheet Planning and EVE Forecasting 597
Basel Accord Guidance on EVE Analysis 600
Principles of Managing Interest Rate Risk in the Banking Book 601
Scenario Construction and EVE Analysis 604
Standardized Framework 607
Summary 608
Notes 610
Bibliography 611
Chapter 9 Net Interest Income 613
Interest Income and Expense: Basics 614
Interest Income and Expense for Floating-Rate Instruments 620
Using the Implied Forward Rate 621
Using the Forecasted Rate 631
Incorporating Balance Sheet Change in NII Analysis 638
Runoff View: No New Volume 638
Static View: Replacement of Matured Positions 642
Dynamic View: Incorporation of Business Plan 644
Earning Gap 648
Interest Rate Scenario Analysis 653
Parallel Shocks 654
Non-Parallel Shocks 664
Balance Sheet Type and NII Sensitivity 670
Impact of Interest Rate Options on NII 673
Currency Exchange Rate Scenario Analysis 683
Currency Forward and Interest Rate Parity 683
Exchange Rate Shock Scenarios 687
Net Interest Income Hedging 691
Net Interest Income Risk Limits 697
Required Data and Other Considerations in NII Analysis 699
Basel Accord Guidance on NII Analysis 701
Summary 702
Notes 704
Bibliography 704
Chapter 10 Equity and Earnings at Risk 705
Introduction to Value-at-Risk 706
Variance-Covariance Method 708
Historical Sampling Method 710
Monte Carlo Simulation Method 713
Conditional Value-at-Risk 717
Application of VaR Methodology in ALM 719
Scenario Generation 721
Historical Sampling 721
Monte Carlo Simulation 726
Standard and Generalized Brownian Motion 726
Multi-dimensional Brownian Motion 730
Geometric Brownian Motion 731
Mean-Reverting Brownian Motion 734
Geometric Mean-Reverting Brownian Motion 739
Calibration 743
Equity-at-Risk 743
Interest Rate Risk Factor 744
Component Contribution 748
Approximation Techniques 749
Currency Exchange Rate Risk Factor 752
Sample Size and Convergence 758
Earnings-at-Risk 762
Interest Rate Risk Factor 763
Currency Exchange Rate Risk Factor 769
Summary 775
Notes 776
Bibliography 777
Chapter 11 Liquidity Risk 779
Funding Source and Liquidity Risk 780
Deposits 781
Short-Term Debt 783
Medium-Term Notes 788
Long-Term Debt 789
Securitization 790
Credit and Liquidity Facilities 793
Eurodollar Deposit and Federal Funds Market 795
Other Sources of Funding 796
Short-Term Secured Funding: Repurchase Agreements 796
Repo Basics 796
Repo Margin 800
Collateral Delivery Methods and Triparty Repo 801
Use of Repo 802
Security Lending 807
Repo and Liquidity Risk 809
Managing Liquidity Risk of Repo 811
Cash Flow Gap Analysis and Liquidity Stress Tests 816
Cash Flow Gap: Business-as-Usual 823
Cash Flow Gap: Idiosyncratic Stress 833
Cash Flow Gap: Market-Wide Stress 841
Cash Flow Gap: Multi-Currency 849
Funding Concentration Risk 854
Basel Accord Liquidity Risk Monitoring Tools 855
Liquidity Coverage Ratio 856
High-Quality Liquid Asset 857
Total Net Cash Outflows in Next 30 Days 859
Net Stable Funding Ratio 873
Available Stable Funding 874
Required Stable Funding 874
Intraday Liquidity 884
Early Warning Indicators 892
Liquidity Contingency Plan 893
Summary 893
Notes 896
Bibliography 897
Chapter 12 Funds Transfer Pricing 899
Funds Transfer Pricing: Basics 900
Pool Method 906
Matched Maturity Method 910
FTP Rate for Fixed-Rate Maturing Products 910
Weighted Average Method 913
Duration Method 914
Refinancing Method 915
FTP Rate for Floating-Rate Maturing Products 917
FTP Rate for Non-Maturing Products 920
Behavioral Model Method 920
Replicating Model Method 930
Components of FTP Rate 932
Characteristics of a Good FTP System 934
Summary 936
Notes 938
Bibliography 938
Appendix: Elements of Probability and Statistics 939
Index 1003
