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Interest Rate Modelling




Interest Rate Modelling

Jessica James, Nick Webber

ISBN: 978-0-471-97523-6 April 2000 676 Pages

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As interest rate markets continue to innovate and expand it is becoming increasingly important to remain up-to-date with the latest practical and theoretical developments. This book covers the latest developments in full, with descriptions and implementation techniques for all the major classes of interest rate models-both those actively used in practice as well as theoretical models still 'waiting in the wings'.

Interest rate models, implementation methods and estimation issues are discussed at length by the authors as are important new developments such as kernel estimation techniques, economic based models, implied pricing methods and models on manifolds.

Providing balanced coverage of both the practical use of models and the theory that underlies them, Interest Rate Modelling adopts an implementation orientation throughout, making it an ideal resource for both practitioners and researchers.
Part 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;

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;

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;

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

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



Glossary of mathematical, market and model terms


Author Index

Subject Index
"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#" 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#