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