Interest Rate Modelling

JESSICA JAMES is Head of Research for Bank One's Strategic Risk Management group, based in the UK. Jessica started life as a physicist at Manchester University and completed her DPhil in Theoretical Atomic and Nuclear Physics at Christ Church, Oxford, under Professor Sandars. After a year as a college lecturer at Trinity, Oxford, she began work at he First National Bank of Chicago, now Bank One, where she still works. She is well known as a speaker on the conference circuit, lecturing on a variety of topics such as VaR, capital allocation, credit derivatives and interest rate modelling, and ahs published articles on various aspects of financial modelling. NICK WEBBER is a lecturer in Finance at Warwick Business School. Prior to his academic career, Nick has had extensive experience in the industrial and commercial world in operational research and computing. After obtaining a PhD in Theoretical Physics from Imperial College he began research into financial options. His main area of research centres on interest rate modelling and computational finance. He ahs taught practitioner and academic course for many years, chiefly on options and interest rates.

• 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

"Interest Rate Modelling is an encyclopedic treatment of interest rates and their related financial derivatives. It combines advanced theory with extensive and down-to-earth data analysis in a way which is truly unique. For practitioners, students and scholars in the field, this impressive wok will be the standard reference for years to come.", Professor Tomas Bjork, , Stockholm School of Economics#"...an excellent book. I am particularly pleased by its breadth and range of topics...the reader is provided with an informative and readable exposition.", Dr Farshid Jamshidian, , NetAnalytic#"I particularly like the strong emphasis on the practicalities and calibration of interest rate models. This book will be invaluable as a comprehensive reference to students, researchers, and practitioners.", Professor Francis Longstaff, , The Anderson School at UCLA#"This is a carefully written, scholarly but fascinating presentation of the field of Interest Rate Modelling. It combines the best of two worlds: the rigour expected from finance in acamedia with the relevance expected from finance in practice. James and Webber are truly masters of their market since this book is surely a must-buy for both researchers and practitioners. If only all finance books were written with this care and attention to detail.", Dr Neil Johnson, , Clarendon Laboratory, Oxford#"Today, interest rates are key economic instruments. This is a mammoth treatise and must surely rank as one of the most comprehensive available on the topic. Anyone interested in modelling or simulating the behaviour of interest rates, be they practitioner, economist, mathematician or new entrant to the subject, will find within a wealth of pertinent material.", Professor Peter Richmond, , Trinity College Dublin#