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Full Description
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.
Contents
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;
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
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