Interest Rate Modelling Book

Part 1: Introduction to interest rate modelling
1. Introduction to interest rates
1.1 Interest rate behaviour
1.2 Basic concepts
1.3 Interest rate markets
1.4 Historical and current data
1.5 Uses of interest rate models
1.6 Conclusion
2. Interest rates in history
2.1 Interest rates in monetary history
2.2 Characteristics of interest rate behaviour
3. Introduction to interest rate modelling
3.1 Yield curve basics
3.2 Describing interest rate processes
3.3 Introducton to interest rate models
3.4 Categories of interest rate model
3.5 The role of the short rate
4. Interest rate models: theory
4.1 Summary of valuation
4.2 A theoretical market framework
4.3 Fundamentals of pricing
4.4 valuing by change of numeraire
4.5 Derivatives in the extended Vasicek model
5. Basic modelling tools
5.1 Introduction to valuation
5.2 Introduction to estimation
5.3 Statistical tests
5.4 Yield curve stripping
5.5 The convexity adjustment
6. Densities and distributions
6.1 The density function
6.2 Kernel methods
6.3 Boundary behaviour
6.4 Interest rate models at extreme values of interest rates
6.5 Tail distributions
Part II Interest rate models
7. Affine models
7.1 Affine term structure models
7.2 Interpreting the state variables
7.3 Types of affine model
7.4 Examples of one-factor affine models
7.5 Examples of n-factor affine models
7.6 A general framework for affine models
8. Market models and the Heath, Jarrow and Morton framework
8.1 Introduction to the Heath, Jarrow and Morton model
8.2 Volatility functions in HJM
8.3 Market models
8.4 General marketmodels
9. Other interest rate models
9.1 Consol models
9.2 Price kernet models
9.3 Positive interest rate models
9.4 Non-linear models
10. General formulations of interest rate models
10.1 Jump processes
10.2 Random field models
10.3 A general model
10.4 Jump models
11. Economic models
11.1 Economics and interest rates
11.2 An economically motivated financial model of interest rates
11.3 An IS-LM based model
11.4 IS-LM, hyperinflation and extended Vasicek
11.5 The general equilibrium framework
11.6 Interpreting the price kernel
Part III Valuation methods
12. Finite difference methods
12.1 The Feynman-Kac Equation
12.2 Discretising the PDE
12.3 Simplifying the PDE
12.4 Explicit methods
12.5 Implicit methods
12.6 The Crank-Nicolson method
12.7 Comparison of methods
12.8 Implicit boundary conditions
12.9 Fitting to an initial term structure
12.10 Finite difference methods in N dimensions
12.11 Operator splitting
12.12 A two-dimensional PDE
12.13 Solving a PDDE
13. Valuation: the Monte Carlo method
13.1 The basic Monte Carlo method
13.2 Speed-up methods
13.3 Sampling issues
13.4 Simulation methods for HJM models
14. Lattice methods
14.1 Introduction to lattice methods
14.2 Issues in constructing a lattice
14.3 Examples of lattice methods
14.4 Calibration to market prices
14.5 The explicit finite difference method
14.6 Lattices and the Monte Carlo method
14.7 Non-recombining lattices
14.8 Conclusions
Part IV Calibration and estimation
15. Modelling the yield curve
15.1 Stripping the yield curve
15.2 Fitting using parameterised curves
15.3 Fitting the yield curve using splines
15.4 Nelson and Siegel curves
15.5 Comparison of families of curves
15.6 Kernel methods of yield curve estimations
15.7 LP and regression methods
16. Principal components analysis
16.1 Volatility structures
16.2 Identifying empirical volatility factors
16.3 Calibrating whole yield curve methods
16.4 Processes on manifolds
16.5 Analysis of dynamical systems
16.6 Conclusions
17. Estimation methods: GMM and ML
17.1 GMM estimation
17.2 Implementation issues
17.3 The efficient method of moments (EMM)
17.4 Maximum likelihood methods
17.5 Hierarchy of procedures
18. Further estimation methods
18.1 Introduction
18.2 Filtering approaches to estimation
18.3 The extended Kalman Filter
18.4 GARCH models
18.5 Extensions of GARCH
18.6 Interest rate models and GARCH
18.7 Artificial neural nets (ANNs)
19. Interest rates and implied pricing
19.1 Problems with interest rate models
19.2 Key relationships
19.3 The interest rate case
19.4 The implied pricing method
19.5 Regularisation functions
19.6 Patching tails onto pricing densities
Afterword
Notation
Glossary of mathematical, market and model terms
References
Author Index
Subject Index