Asset-Liability and Liquidity Management

POOYA FARAHVASH is vice president of Treasury Modeling and Analytics at American Express Company overseeing development of models used in ALM, liquidity risk management, stress testing, and deposit products. He previously worked at investment bank Jefferies in liquidity risk management and at CIT Group in asset-liability management. His experience in the banking industry is focused in treasury department activities, specifically in areas of interest rate risk, liquidity risk, asset-liability management, deposit modeling, and economic capital. Dr. Farahvash is also an adjunct instructor at New York University, teaching analytical courses. He received his PhD degree in Industrial and Systems Engineering and MS degree in Statistics both from Rutgers University, New Jersey. He currently lives in New York City.

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