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9780470325896

Interest Rate Modelling

by ;
  • ISBN13:

    9780470325896

  • ISBN10:

    0470325895

  • Format: eBook
  • Copyright: 2008-04-01
  • Publisher: Wiley
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Summary

As interest rate markets continue to innovate and expand it is becoming increasingly important to remain up-to-date with the latest practical and theoretical developments. This book covers the latest developments in full, with descriptions and implementation techniques for all the major classes of interest rate models-both those actively used in practice as well as theoretical models still 'waiting in the wings'. Interest rate models, implementation methods and estimation issues are discussed at length by the authors as are important new developments such as kernel estimation techniques, economic based models, implied pricing methods and models on manifolds. Providing balanced coverage of both the practical use of models and the theory that underlies them, Interest Rate Modelling adopts an implementation orientation throughout, making it an ideal resource for both practitioners and researchers.

Table of Contents

Introduction to interest rate modelling
Introduction to interest rates
Interest rate behaviour
Basic concepts
Interest rate markets
Historical and current data
Uses of interest rate models
Conclusion
Interest rates in history
Interest rates in monetary history
Characteristics of interest rate behaviour
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
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
Basic modelling tools
Introduction to valuation
Introduction to estimation
Statistical tests
Yield curve stripping
The convexity adjustment
Densities and distributions
The density function
Kernel methods
Boundary behaviour
Interest rate models at extreme values of interest rates
Tail distributions
Interest rate models
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
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
Other interest rate models
Consol models
Price kernet models
Positive interest rate models
Non-linear models
General formulations of interest rate models
Jump processes
Random field models
A general model
Jump models
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
Valuation methods
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
Valuation: the Monte Carlo method
The basic Monte Carlo method
Speed-up methods
Sampling issues
Simulation methods for HJM models
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
Calibration and estimation
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
Principal components analysis
Volatility structures
Identifying empirical volatility factors
Calibrating whole yield curve methods
Processes on manifolds
Analysis of dynamical systems
Conclusions
Estimation methods: GMM and ML
GMM estimation
Implementation issues
The efficient method of moments (EMM)
Maximum likelihood methods
Hierarchy of procedures
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)
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
Table of Contents provided by Publisher. All Rights Reserved.

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