Interest Rate Modelling

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