Interest‐Rate Modelling

Abstract

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 market models 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