Description
Book SynopsisThis volume covers developments in the interest rate markets, with descriptions and implementation techniques for all the major classes of interest rate models. It covers those models already in practice, as well as theoretical models.
Trade Review"Interest Rate Modelling is an encyclopedic treatment of interest rates and their related financial derivatives. It combines advanced theory with extensive and down-to-earth data analysis in a way which is truly unique. For practitioners, students and scholars in the field, this impressive wok will be the standard reference for years to come.", Professor Tomas Bjork, , Stockholm School of Economics#"...an excellent book. I am particularly pleased by its breadth and range of topics...the reader is provided with an informative and readable exposition.", Dr Farshid Jamshidian, , NetAnalytic#"I particularly like the strong emphasis on the practicalities and calibration of interest rate models. This book will be invaluable as a comprehensive reference to students, researchers, and practitioners.", Professor Francis Longstaff, , The Anderson School at UCLA#"This is a carefully written, scholarly but fascinating presentation of the field of Interest Rate Modelling. It combines the best of two worlds: the rigour expected from finance in acamedia with the relevance expected from finance in practice. James and Webber are truly masters of their market since this book is surely a must-buy for both researchers and practitioners. If only all finance books were written with this care and attention to detail.", Dr Neil Johnson, , Clarendon Laboratory, Oxford#"Today, interest rates are key economic instruments. This is a mammoth treatise and must surely rank as one of the most comprehensive available on the topic. Anyone interested in modelling or simulating the behaviour of interest rates, be they practitioner, economist, mathematician or new entrant to the subject, will find within a wealth of pertinent material.", Professor Peter Richmond, , Trinity College Dublin#
Table of ContentsPart I: Introduction to interest rate modelling
1. Introduction to interest rates
Interest rate behaviour;
Basic concepts;
Interest rate markets;
Historical and current data;
Uses of interest rate models;
Conclusion
2. Interest rates in history
Interest rates in monetary history;
Characteristics of interest rate behaviour
3. Introduction to interest rate modelling
Yield curve basics;
Describing interest rate processes;
Introducton to interest rate models;
Categories of interest rate model;
The role of the short rate
4. Interest rate models: theory
Summary of valuation
A theoretical market framework;
Fundamentals of pricing; valuing by change of numeraire;
Derivatives in the extended Vasicek model
5. Basic modelling tools
Introduction to valuation;
Introduction to estimation;
Statistical tests;
Yield curve stripping;
The convexity adjustment
6. Densities and distributions
The density function;
Kernel methods;
Boundary behaviour;
Interest rate models at extreme values of interest rates;
Tail distributions
Part II Interest rate models
7. Affine models
Affine term structure models;
Interpreting the state variables;
Types of affine model;
Examples of one-factor affine models;
Examples of n-factor affine models;
A general framework for affine models
8. Market models and the Heath, Jarrow and Morton framework
Introduction to the Heath, Jarrow and Morton model;
Volatility functions in HJM;
Market models;
General market models
9. Other interest rate models
Consol models;
Price kernet models;
Positive interest rate models;
Non-linear models
10. General formulations of interest rate models
Jump processes;
Random field models;
A general model;
Jump models
11. Economic models
Economics and interest rates
An economically motivated financial model of interest rates;
An IS-LM based model;
IS-LM, hyperinflation and extended Vasicek;
The general equilibrium framework;
Interpreting the price kernel
Part III Valuation methods
12. Finite difference methods
The Feynman-Kac Equation;
Discretising the PDE;
Simplifying the PDE;
Explicit methods;
Implicit methods;
The Crank-Nicolson method;
Comparison of methods;
Implicit boundary conditions;
Fitting to an initial term structure;
Finite difference methods in N dimensions;
Operator splitting;
A two-dimensional PDE;
Solving a PDDE
13. Valuation: the Monte Carlo method
The basic Monte Carlo method;
Speed-up methods;
Sampling issues;
Simulation methods for HJM models
14. Lattice methods
Introduction to lattice methods;
Issues in constructing a lattice;
Examples of lattice methods;
Calibration to market prices;
The explicit finite difference method;
Lattices and the Monte Carlo method;
Non-recombining lattices;
Conclusions
Part IV Calibration and estimation
15. Modelling the yield curve
Stripping the yield curve;
Fitting using parameterised curves;
Fitting the yield curve using splines;
Nelson and Siegel curves;
Comparison of families of curves;
Kernel methods of yield curve estimations;
LP and regression methods
16. Principal components analysis
Volatility structures;
Identifying empirical volatility factors;
Calibrating whole yield curve methods;
Processes on manifolds;
Analysis of dynamical systems;
Conclusions
17. Estimation methods: GMM and ML
GMM estimation;
Implementation issues;
The efficient method of moments (EMM);
Maximum likelihood methods;
Hierarchy of procedures
18. Further estimation methods
Introduction;
Filtering approaches to estimation;
The extended Kalman Filter;
GARCH models;
Extensions of GARCH;
Interest rate models and GARCH;
Artificial neural nets (ANNs)
19. Interest rates and implied pricing
Problems with interest rate models;
Key relationships;
The interest rate case;
The implied pricing method;
Regularisation functions;
Patching tails onto pricing densities
Afterword
Notation
Glossary of mathematical, market and model terms
References
Author Index
Subject Index
