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Term-Structure Models: a Review
Riccardo Rebonato
QUARC (QUAntitativeResearch Centre) - Royal Bank of Scotland
Oxford University - OCIAM
February 25, 2003
1 Introduction
1.1 Justi¯cation for Another Review of Interest-Rate Models
1.2 Plan of the Survey
2 Market Practice
2.1 Different Users of Term-Structure Models
2.2 Statistical Information, Hedging Practice and Model Evolution
2.3 Reasons for Inertia to Model Changes
2.4 In-Model and Out-of-Model Hedging
3 A Unified Modelling Approach
3.1 The Mathematical Setting
3.2 Different Descriptions
3.3 Equivalence of the Di®erent Approaches
3.4 The Relative Risk Density Process and Derivatives Pricing
3.5 From Absolute to Relative Pricing
4 Phase 1: The Black-and-Scholes/Merton Approach
4.1 Adapting the BS/M Framework to Interest-Rate Derivatives
4.2 The Pull-To-Par Problem
4.3 From Black-and-Scholes to Black
4.4 From Price Models to Rate and Yield Models
4.5 The Need for a Coherent Model
5 Phase 2: First-Generation Yield-Curve Models
5.1 Vasicek and CIR
5.2 Reasons for the Good Performance of Short-Rate Models
6 Phase 3: Second-Generation Yield Curve Models
6.1 Fitting the Yield Curve
6.3 Tree-Based Models
6.4 The Dimensionality of the Underlying Drivers
7 Phase 4: Third-Generation Yield Curve Models
7.1 The HJM Results
7.2 The LIBOR Market Models
7.3 The Early-Exercise Problem
8 Variations on the LMM Theme
8.1 Low-Dimensionality Versions of the HJM Model
8.2 Low-Dimensionality Markov Market Models
9 Other Approaches
9.1 Positive-Rate Models
10 Phase 5: Accounting for Smiles
10.1 First-Generation Smiles
10.2 Second-Generation Smiles
10.3 The Poverty of Pure Price Fitting
10.4 Decomposition of the Volatility Drivers
10.5 The Proposed Approaches
11 The Calibration Debate
11.1 Historical versus Implied Calibration
11.2 The Logical Underpinning of the Implied Approach
11.3 Are Interest-Rate Derivatives Market Information-ally Efficient?
11.4 Conclusions
12 Summary and Further Perspectives
12.1 Comparison of Pricing and Modelling Practices
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