Interest Rate ModellingISBN: 978-0-471-97523-6
Hardcover
676 pages
June 2000
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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
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