Interest rate modelling. (Q2756617)

This book bring together all the main strands of thought in interest rate modelling and implementation. The traditional complete-market arbitrage pricing approach is covered in detail, both from the perspective of short-rate models and using the more modern martingale approach. The general equilibrium approach is given, a no less important treatment as well, and such concepts as the price kernel are clearly and throughly treated. The authors have given a first, and important, contribution towards a much-needed synthesis between the `explanatory view' (where the term structure of rates has to be determined endogenously) and the 'descriptive school' (which takes the market prices as an exogenous given). Those interested in the field will be able to use this book to assist in understanding and implementing virtually any interest rate model. Practitioners will find advanced implementation and calibration methods and a very full review of existing term structure models. Academics will find expositions of the theoretical underpinnings and discussions on research issues. NEWLINENEWLINENEWLINEMuch of the material in this book has been previously published only in academic or finance industry journals, or may only have been available in working paper form. NEWLINENEWLINENEWLINEThe content reflects the main divisions in the field. NEWLINENEWLINENEWLINEPart I (Chapters 1-6) `Introduction to interest rate modelling' gives an intuitive description of the theoretical background to interest rate modelling. The ideas introduced here are elaborated upon in later parts. Chapter 1 is introductory. It presents basic ideas of interest rates and the markets. Chapter 2 briefly reviews the history of interest rates, which have existed, as far back as records of human civilization go. Chapter 3 introduces basic interest rate instruments and general modelling features. Some features of the financial markets are discussed and simple methods of extracting interest rate data from the market prices are described. The concept of the yield curve is discussed in more detail. Some simple interest rate models are presented and compared. Chapter 4 deals with the mathematical theory of underpinning interest rate modelling. It introduces the key ideas of martingale measure, numeraire, changes of measure, etc. Chapter 5 introduces some basic modelling tools; valuation using PDEs and simulation, estimation, and yield curve stripping. More useful tools are described in Chapter 6 `Densities and Distributions'. NEWLINENEWLINENEWLINEPart II `Interest rate models'. Chapters: 7. Affine models; 8. Market models and the Heath, Jarrow and Morton (HJM) framework; 9. Other interest rate models; 10. General formulations of interest rate models; 11. Economic models. This part concentrates on interest rate models themselves. All the main categories of the model are considered and popular models are discussed in details. Historically, models have been classified as factor models (using a number of underlying factors to generate rate dynamics) or as whole yield curve models (modelling the evolution of the entire curve itself). Affine models are among the most tractable type of interest rate models. These models are probably the most popular models in implementation. More sophisticated applications may require the use of a whole yield curve model. Recently Brace, Gatarek and Musiela (BGM) and market models have become quite common. These models focus on the evolution of market-quoted rates themselves. They may be even easier to use than an affine model if one is simply using them as a substitute for Black's formulae; more difficult applications need less tractable methods. Positive rate models and price kernel models are among those explored in Chapter 9. These models have attracted a great deal of attention recently and further developments are likely. Chapter 10 looks at some of the other more general attempts that have been made to model interest rate behaviour, including infinite factor random field models and models with jumps. The final chapter of Part II looks more particularly at models with an economic basis of some sort. The general equilibrium framework is described, as are models based on ideas from macro-economics. NEWLINENEWLINENEWLINEIn Part III (Chapters 12-14) the main valuation methods, namely methods of extracting actual prices from an interest rate model are discussed: finite difference methods, Monte Carlo methods and lattice methods. Monte Carlo methods are relatively straightforward methods of valuing path-dependent options of European type although fast practical implementations can be very sophisticated. These are described in Chapter 13. Finite difference methods are discussed in Chapter 12. These methods can value American style options and can sometimes be used to value path-dependent options. The third category of valuation method-lattice methods are simpler to implement than finite difference methods but tend to be model-dependent (see Chapter 14). NEWLINENEWLINENEWLINEPart IV (Chapters 15-19) deals with all the estimation and calibration techniques used in the market. Chapter 15 discusses how the yield curve may be extracted from market data using non-parametric techniques, including spline methods. In Chapter 16 it is discussed how a series of fitted yield curves can be used to estimate volatility functions for whole yield curve models. The technique, principal components analysis (PCA), can also be applied to current market prices to calibrate directly to implied volatility and covariance structures. Chapters 17 and 18 are about estimating model parameters from historical data. Since interest rate distributions are not normal, a number of sophisticated techniques are necessary to find the values of the floating parameters. The general method of moments and maximum likelihood techniques, including simulation based approaches are described. Chapter 18 looks at filtering methods and at GARCH based methods. Chapter 19 investigates implied pricing. The drift and volatility functions of an interest rate process may be extracted from market prices. This chapter discusses how a model may be calibrated to the entire volatility surface, and explains how a number of the difficulties involved may be overcome. NEWLINENEWLINENEWLINEThe book is intended to be suitable for use on Masters and Doctoral courses, and may serve as a reference text for more advanced undergraduate and MBA courses.