Frontmatter Page xii Monday, March 8, 2004 10:06 AM
xii ContentsThe Discount Function 606
Forward Rates 607
Swap Curve 608
Classical Economic Theories About the Determinants of the
Shape of the Term Structure 612
Expectations Theories 613
Market Segmentation Theory 618
Bond Valuation Formulas in Continuous Time 618
The Term Structure of Interest Rates in Continuous Time 623
Spot Rates: Continuous Case 624
Forward Rates: Continuous Case 625
Relationships for Bond and Option Valuation 626
The Feynman-Kac Formula 627
Multifactor Term Structure Model 632
Arbitrage-Free Models versus Equilibrium Models 634
Examples of One-Factor Term Structure Models 635
Two-Factor Models 638
Pricing of Interest-Rate Derivatives 638
The Heath-Jarrow-Morton Model of the Term Structure 640
The Brace-Gatarek-Musiela Model 643
Discretization of Itô Processes 644
Summary 646
CHAPTER 21
Bond Portfolio Management 649
Management versus a Bond Market Index 649
Tracking Error and Bond Portfolio Strategies 651
Risk Factors and Portfolio Management Strategies 652
Determinants of Tracking Error 654
Illustration of the Multifactor Risk Model 654
Liability-Funding Strategies 661
Cash Flow Matching 664
Portfolio Immunization 667
Scenario Optimization 672
Stochastic Programming 673
Summary 677
CHAPTER 22
Credit Risk Modeling and Credit Default Swaps 679
Credit Default Swaps 679
Single-Name Credit Default Swaps 680
Basket Default Swaps 681
Legal Documentation 683
Credit Risk Modeling: Structural Models 683
The Black-Scholes-Merton Model 685
Geske Compound Option Model 690
Barrier Structural Models 694
Advantages and Drawbacks of Structural Models 696
Credit Risk Modeling: Reduced Form Models 696