Description
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 Deltat-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
