1st Edition
Robust Libor Modelling and Pricing of Derivative Products
One of Riskbook.com's Best of 2005 - Top Ten Finance Books
The Libor market model remains one of the most popular and advanced tools for modelling interest rates and interest rate derivatives, but finding a useful procedure for calibrating the model has been a perennial problem. Also the respective pricing of exotic derivative products such as Bermudan callable structures is considered highly non-trivial. In recent studies, author John Schoenmakers and his colleagues developed a fast and robust implied method for calibrating the Libor model and a new generic procedure for the pricing of callable derivative instruments in this model.
Within a compact, self-contained review of the requisite mathematical theory on interest rate modelling, Robust Libor Modelling and Pricing of Derivative Products introduces the author's new approaches and their impact on Libor modelling and derivative pricing. Discussions include economically sensible parametrisations of the Libor market model, stability issues connected to direct least-squares calibration methods, European and Bermudan style exotics pricing, and lognormal approximations suitable for the Libor market model.
A look at the available literature on Libor modelling shows that the issues surrounding instabilty of calibration and its consequences have not been well documented, and an effective general approach for treating Bermudan callable Libor products has been missing. This book fills these gaps and with clear illustrations, examples, and explanations, offers new methods that surmount some of the Libor model's thornier obstacles.
Elements of Arbitrage Theory and Derivative Pricing
Modelling of Effective Forward Rates
Pricing of Caps and Swaptions in Libor and Swap Market Models
PARAMETRISATION OF THE LIBOR MARKET MODEL
General Volatility Structures
(Quasi) Time-Shift Homogeneous Models
Parametrisation of Correlation Structures
Some Possible Applications of Parametric Structures
IMPLIED CALIBRATION OF A LIBOR MARKET MODEL TO CAPS AND SWAPTIONS
Orientation and General Aspects
Assessment of the Calibration Problem
LSq Calibration and Stability Issues in Practice
Regularisation via a Collateral Market Criterion
Calibration of a Time-Shift Homogeneous LMM
PRICING OF EXOTIC EUROPEAN STYLE PRODUCTS
Exotic European Style Products
Factor Dependence of Exotic Products
Case Studies
PRICING OF BERMUDAN STYLE LIBOR DERIVATIVES
Orientation
The Bermudan Pricing Problem
Backward Construction of the Exercise Boundary
Iterative Construction of the Optimal Stopping Time
Duality; From Tight Lower Bounds to Tight Upper Bounds
Monte Carlo Simulation of Upper Bounds
Numerical Evaluation of Bermudan Swaptions by Different Methods
Efficient Monte Carlo Construction of Upper Bounds
Multiple Callable Structures
PRICING LONG DATED PRODUCTS VIA LIBOR APPROXIMATIONS
Introduction
Different Lognormal Approximations
Direct Simulation of Lognormal Approximations
Efficiency Gain with Respect to SDE Simulation; an Optimal
Simulation Program
Practical Simulation Examples
Summarisation and Final Remarks
APPENDIX
Glossary of Stochastic Calculus
Minimum Search Procedures
Additional Proofs
REFERENCES
INDEX
Biography
Schoenmakers\, John
"Schoenmakers' text is the definitive text on the Libor market model (and related models). He briefly reviews financial engineering theory, explains the HJM framework, describes several Libor market model implementations, and illustrates with practical pricing problems. … His writing is minimalist but extremely well organized. Ideas progress from one to another in a clear mathematical progressing of theorems and proofs. … For serious implementers, Schoenmakers is the essential book. If you have the financial engineering background to follow it, you will find his presentation a delightful read-clean, rigorous, and masterful."
-Glyn Holton, Contingency Analysis, 2005
"This book provides an introduction to the Libor market model, one of the current tools for modeling interest rates and interest rate derivatives."
-Short Book Reviews of the ISI
