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Modern Pricing of Interest-Rate Derivatives : The LIBOR Market Model and Beyond - Riccardo Rebonato

Modern Pricing of Interest-Rate Derivatives

The LIBOR Market Model and Beyond


Published: 24th November 2002
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In recent years, interest-rate modeling has developed rapidly in terms of both practice and theory. The academic and practitioners' communities, however, have not always communicated as productively as would have been desirable. As a result, their research programs have often developed with little constructive interference. In this book, Riccardo Rebonato draws on his academic and professional experience, straddling both sides of the divide to bring together and build on what theory and trading have to offer.

Rebonato begins by presenting the conceptual foundations for the application of the LIBOR market model to the pricing of interest-rate derivatives. Next he treats in great detail the calibration of this model to market prices, asking how possible and advisable it is to enforce a simultaneous fitting to several market observables. He does so with an eye not only to mathematical feasibility but also to financial justification, while devoting special scrutiny to the implications of market incompleteness.

Much of the book concerns an original extension of the LIBOR market model, devised to account for implied volatility smiles. This is done by introducing a stochastic-volatility, displaced-diffusion version of the model. The emphasis again is on the financial justification and on the computational feasibility of the proposed solution to the smile problem. This book is must reading for quantitative researchers in financial houses, sophisticated practitioners in the derivatives area, and students of finance.

"Rebonato's writing style is probably the most elegant I have ever seen in a quantitative finance book. His ideas are conveyed in a brief and clear manner... I thoroughly enjoyed this book since it allowed me to discover a whole new world in a fast and painless fashion. I would therefore recommend it to everyone who has any interest in the fascinating universe of fixed-income derivatives."--Alireza Javaheri, Quantitative Finance

Introductionp. xi
Acknowledgementsp. xvii
The Structure of the LIBOR Market Modelp. 1
Putting the Modern Pricing Approach in Perspectivep. 3
Historical Developmentsp. 3
Some Important Remarksp. 21
The Mathematical and Financial Set-upp. 25
The Modelling Frameworkp. 25
Definition and Valuation of the Underlying Plain-Vanilla Instrumentsp. 28
The Mathematical and Financial Description of the Securities Marketp. 40
Describing the Dynamics of Forward Ratesp. 57
A Working Framework for the Modern Pricing Approachp. 57
Equivalent Descriptions of the Dynamics of Forward Ratesp. 65
Generalization of the Approachp. 79
The Swap-Rate-Based LIBOR Market Modelp. 83
Characterizing and Valuing Complex LIBOR Productsp. 85
The Types of Product That Can be Handled Using the LIBOR Market Modelp. 85
Case Study: Pricing in a Three-Forward-Rate, Two-Factor Worldp. 96
Overview of the Results So Farp. 107
Determining the No-Arbitrage Drifts of Forward Ratesp. 111
General Derivation of the Drift Termsp. 112
Expressing the No-Arbitrage Conditions in Terms of Market-Related Quantitiesp. 118
Approximations of the Drift Termsp. 123
Conclusions 131
The Inputs to the General Frameworkp. 133
Instantaneous Volatilitiesp. 135
Introduction and Motivationp. 135
Instantaneous Volatility Functions: General Resultsp. 141
Functional Forms for the Instantaneous Volatility Function - Financial Implicationsp. 153
Analysis of Specific Functional Forms for the Instantaneous Volatility Functionsp. 167
Appendix I - Why Specification (6.11c) Fails to Satisfy Joint Conditionsp. 171
Appendix II - Indefinite Integral of the Instantaneous Covariancep. 171
Specifying the Instantaneous Correlation Functionp. 173
General Considerationsp. 173
Empirical Data and Financial Plausibilityp. 180
Intrinsic Limitations of Low-Dimensionality Approachesp. 185
Proposed Functional Forms for the Instantaneous Correlation Functionp. 189
Conditions for the Occurrence of Exponential Correlation Surfacesp. 196
A Semi-Parametric Specification of the Correlation Surface 204
Calibration of the LIBOR Market Modelp. 209
Fitting the Instantaneous Volatility Functionsp. 211
General Calibration Philosophy and Plan of Part IIIp. 211
A First Approach to Fitting the Caplet Market: Imposing Time-Homogeneityp. 214
A Second Approach to Fitting the Caplet Market: Using Information from the Swaption Matrixp. 218
A Third Approach to Fitting the Caplet Market: Assigning a Future Term Structure of Volatilitiesp. 226
Resultsp. 231
Conclusionsp. 248
Simultaneous Calibration to Market Caplet Prices and to an Exogenous Correlation Matrixp. 249
Introduction and Motivationp. 249
An Optimal Procedure to Recover an Exogenous Target Correlation Matrixp. 254
Results and Discussionp. 260
Conclusionsp. 274
Calibrating a Forward-Rate-Based LIBOR Market Model to Swaption Pricesp. 276
The General Contextp. 276
The Need for a Joint Description of the Forward-and Swap-Rate Dynamicsp. 280
Approximating the Swap-Rate Instantaneous Volatilityp. 294
Computational Results on European Swaptionsp. 306
Calibration to Co-Terminal European Swaption Pricesp. 312
An Application: Using an FRA-Based LIBOR Market Model for Bermudan Swaptionsp. 318
Quality of the Numerical Approximation in Realistic Market Casesp. 326
Beyond the Standard Approach: Accounting for Smilesp. 331
Extending the Standard Approach - I: CEV and Displaced Diffusionp. 333
Practical and Conceptual Implications of Non-Flat Volatility Smilesp. 333
Calculating Deltas and Other Risk Derivatives in the Presence of Smilesp. 342
Accounting for Monotonically Decreasing Smilesp. 349
Time-Homogeneity in the Context of Di
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780691089737
ISBN-10: 0691089736
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 488
Published: 24th November 2002
Publisher: Princeton University Press
Country of Publication: US
Dimensions (cm): 23.5 x 15.2  x 3.81
Weight (kg): 0.85