| Introduction | p. xi |
| Acknowledgements | p. xvii |
| The Structure of the LIBOR Market Model | p. 1 |
| Putting the Modern Pricing Approach in Perspective | p. 3 |
| Historical Developments | p. 3 |
| Some Important Remarks | p. 21 |
| The Mathematical and Financial Set-up | p. 25 |
| The Modelling Framework | p. 25 |
| Definition and Valuation of the Underlying Plain-Vanilla Instruments | p. 28 |
| The Mathematical and Financial Description of the Securities Market | p. 40 |
| Describing the Dynamics of Forward Rates | p. 57 |
| A Working Framework for the Modern Pricing Approach | p. 57 |
| Equivalent Descriptions of the Dynamics of Forward Rates | p. 65 |
| Generalization of the Approach | p. 79 |
| The Swap-Rate-Based LIBOR Market Model | p. 83 |
| Characterizing and Valuing Complex LIBOR Products | p. 85 |
| The Types of Product That Can be Handled Using the LIBOR Market Model | p. 85 |
| Case Study: Pricing in a Three-Forward-Rate, Two-Factor World | p. 96 |
| Overview of the Results So Far | p. 107 |
| Determining the No-Arbitrage Drifts of Forward Rates | p. 111 |
| General Derivation of the Drift Terms | p. 112 |
| Expressing the No-Arbitrage Conditions in Terms of Market-Related Quantities | p. 118 |
| Approximations of the Drift Terms | p. 123 |
| Conclusions 131 | |
| The Inputs to the General Framework | p. 133 |
| Instantaneous Volatilities | p. 135 |
| Introduction and Motivation | p. 135 |
| Instantaneous Volatility Functions: General Results | p. 141 |
| Functional Forms for the Instantaneous Volatility Function - Financial Implications | p. 153 |
| Analysis of Specific Functional Forms for the Instantaneous Volatility Functions | p. 167 |
| Appendix I - Why Specification (6.11c) Fails to Satisfy Joint Conditions | p. 171 |
| Appendix II - Indefinite Integral of the Instantaneous Covariance | p. 171 |
| Specifying the Instantaneous Correlation Function | p. 173 |
| General Considerations | p. 173 |
| Empirical Data and Financial Plausibility | p. 180 |
| Intrinsic Limitations of Low-Dimensionality Approaches | p. 185 |
| Proposed Functional Forms for the Instantaneous Correlation Function | p. 189 |
| Conditions for the Occurrence of Exponential Correlation Surfaces | p. 196 |
| A Semi-Parametric Specification of the Correlation Surface 204 | |
| Calibration of the LIBOR Market Model | p. 209 |
| Fitting the Instantaneous Volatility Functions | p. 211 |
| General Calibration Philosophy and Plan of Part III | p. 211 |
| A First Approach to Fitting the Caplet Market: Imposing Time-Homogeneity | p. 214 |
| A Second Approach to Fitting the Caplet Market: Using Information from the Swaption Matrix | p. 218 |
| A Third Approach to Fitting the Caplet Market: Assigning a Future Term Structure of Volatilities | p. 226 |
| Results | p. 231 |
| Conclusions | p. 248 |
| Simultaneous Calibration to Market Caplet Prices and to an Exogenous Correlation Matrix | p. 249 |
| Introduction and Motivation | p. 249 |
| An Optimal Procedure to Recover an Exogenous Target Correlation Matrix | p. 254 |
| Results and Discussion | p. 260 |
| Conclusions | p. 274 |
| Calibrating a Forward-Rate-Based LIBOR Market Model to Swaption Prices | p. 276 |
| The General Context | p. 276 |
| The Need for a Joint Description of the Forward-and Swap-Rate Dynamics | p. 280 |
| Approximating the Swap-Rate Instantaneous Volatility | p. 294 |
| Computational Results on European Swaptions | p. 306 |
| Calibration to Co-Terminal European Swaption Prices | p. 312 |
| An Application: Using an FRA-Based LIBOR Market Model for Bermudan Swaptions | p. 318 |
| Quality of the Numerical Approximation in Realistic Market Cases | p. 326 |
| Beyond the Standard Approach: Accounting for Smiles | p. 331 |
| Extending the Standard Approach - I: CEV and Displaced Diffusion | p. 333 |
| Practical and Conceptual Implications of Non-Flat Volatility Smiles | p. 333 |
| Calculating Deltas and Other Risk Derivatives in the Presence of Smiles | p. 342 |
| Accounting for Monotonically Decreasing Smiles | p. 349 |
| Time-Homogeneity in the Context of Di | |
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