SUMMARY

• Covers interest-rate analysis in the light of increased computer power

• Investigates simulation processes, e.g. random walks and Monte Carlo simulation

• Details the development of three new interest-rate model types including the Markov decision process, extensions and generalisations to the Heath-Jarrow-Morton model and market models

• Makes accessible advanced models that enable modellers to 'complete the market' more efficiently when calculating interest rate securities and options' portfolios

• Analysis of Heath-Jarrow-Morton extensions

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  TABLE OF CONTENTS

CONTENTS

By Lane Hughston

Introduction
Lane Hughston

I. Forward short rate models and their empirical consequences

Chapter 1
Bond Pricing and the Term Structure of Interest Rates
David Heath, Robert Jarrow and Andrew Morton

Chapter 2
Testing the Heath-Jarrow-Morton/Ho-Lee Model of Interest Rate Contingent
Claims Pricing
Björn Flesaker

Chapter 3
Implied Volatility Functions in Arbitrage-Free Term Structure Models
Kaushik I. Amin and Andrew J. Morton

Chapter 4
Volatility Structures of Forward Rates and the Dynamics of the Term
Structure
Peter Ritchken and L Sanakarasubramanian

II. Short rate models new and old

Chapter 5
The Volatility of Short-Term Interest Rates: An Empirical Comparison of
Alternative Models of the Term Structure of Interest Rates
Kalok C. Chan, G. Andrew Karolyi, Francis A. Longstaff and Anthony B.
Sanders

Chapter 6
When is the short rate Markovian?
Andrew Carverhill

Chapter 7
Non-parametric Pricing of Interest Rate Derivative Securities
Yacine Aït-Sahalia

Chapter 8
A Non-parametric Analysis of the Forward Rate Volatilities
Neil Pearson and A. Zhou

Chapter 9
Bond Market Clearing
Oldrich Vasicek

III. Potentials and Positive Interest

Chapter 10
A Theory of the Nominal Term Structure of Interest Rates
George M. Constantinides

Chapter 11
The Potential Approach to the Term Structure of Interest Rates
L. C. G. Rogers

Chapter 12
A Note on the Flesaker-Hughston Model of the Term Structure of Interest
Rates
Marek Rutkowski

Chapter 13
International Models for Interest Rates and Foreign Exchange
Björn Flesaker Lane Hughston

Chapter 14
Markov-Functional Interest Rate Models
Philip Hunt, Joanne Kennedy and Antoon Pelsser

IV. From Market Models to Hilbert space theories of the term structure

Chapter 15
A Term Structure Model and the Pricing of Interest Rate Derivatives
Klaus Sandmann and Dieter Sondermann

Chapter 16
A Yield-Factor Model of Interest Rates
Darrell Duffie, and Raymond M. Kan

Chapter 17
Characterising Gaussian Models of the Term Structure
Douglas Kennedy

Chapter 18
Interest Rate Dynamics and Consistent Forward Rate Curves
Tomas Björk and Bent J. Christensen

Chapter 19
Strings Attached
Jean-Philippe Bouchaud, Nicolas Sagna, Rama Cont, Nicole el-Karoui and Marc
Potters

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  QUOTES

″Provides an excellent view of the various approaches to modelling interest rates that are available in the market...A useful reference for anyone working on interest rates.″
Douglas Long, Principia Partners

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  REVIEW

Reviewed by Douglas Long, Principia Partners

Interest rate modelling is one of the most important and theoretically challenging areas in the mathematical finance arena. Years of research have yet to uncover a model which is generally regarded as being superior to all other available models in the market. This book, edited and introduced by the veteran academic and finance practitioner Lane Hughston, is a collection of articles which charts the various directions that have been taken in modelling interest rates, and in doing so provides a clear snapshot of the current status in the search for this so-called `standard model'.

Hughston manages to distil the large body of research papers available in this area down to a manageable, well-balanced selection of 19 articles, some of which are unpublished or difficult to obtain. This is clear when one notes that the 16 published articles can be found in 10 different journals.

The book is split into an introduction and four sections. The introduction provides a clear general summary of the main concepts when modelling interest rate, and links the selected articles in this collection together. The first section consists of the original seminal HJM article followed by several articles that look empirically at possible volatility structures of the forward rate within the HJM framework. The second group of articles are on the theoretical and empirical aspects of short rate models, although the unpublished article by Pearson and Zhou does fit more naturally into the first part.

In many ways the first two sections of the book complement and bring up-to-date the series of articles presented in the book ″Vasicek and Beyond: Approaches to Building and Applying Interest Rate Models″, a 1996 publication by Risk Books, which was also edited by Hughston.

The remaining sections look at a selection of the alternative models available in the academic literature, which have yet to establish the mainstream popularity associated with short rate models, HJM, and market models. These include the pricing kernel models (potential and positive interest rate approaches), random field interest rate models, and affine multi-factor models. It is also nice to see some important unpublished contributions, particularly the article by Hunt, Kennedy and Pelsser on Markov-Functional Interest Rate Models. Section four also includes the paper by Sandmann and Sondermann, which first sparked interest in the market models.

Overall the book provides an excellent view of the various approaches to modelling interest rates that are available in the market. This book is a useful reference collection for anyone working on interest rates and would be particularly interesting to anyone in search of the `standard model'.

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  AUTHOR BIOGRAPHY

David Heath, Robert Jarrow and Andrew Morton ; Björn Flesaker ; Kaushik I. Amin and Andrew J. Morton ; Peter Ritchken and L Sanakarasubramanian ; Kalok C. Chan, G. Andrew Karolyi, Francis A. Longstaff and Anthony B. Sanders ; Andrew Carverhill ; Yacine Aït-Sahalia ; Neil Pearson and A. Zhou ; Oldrich Vasicek ; George M. Constantinides ; L. C. G. Rogers ; Marek Rutkowski ; Björn Flesaker Lane Hughston ; Philip Hunt, Joanne Kennedy and Antoon Pelsser ; Klaus Sandmann and Dieter Sondermann ; Darrell Duffie, and Raymond M. Kan ; Douglas Kennedy ; Tomas Björk and Bent J. Christensen ; Jean-Philippe Bouchaud, Nicolas Sagna, Rama Cont, Nicole el-Karoui and Marc Potters

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  CONTRIBUTORS

David Heath, Robert Jarrow and Andrew Morton ; Björn Flesaker ; Kaushik I. Amin and Andrew J. Morton ; Peter Ritchken and L Sanakarasubramanian ; Kalok C. Chan, G. Andrew Karolyi, Francis A. Longstaff and Anthony B. Sanders ; Andrew Carverhill ; Yacine Aït-Sahalia ; Neil Pearson and A. Zhou ; Oldrich Vasicek ; George M. Constantinides ; L. C. G. Rogers ; Marek Rutkowski ; Björn Flesaker Lane Hughston ; Philip Hunt, Joanne Kennedy and Antoon Pelsser ; Klaus Sandmann and Dieter Sondermann ; Darrell Duffie, and Raymond M. Kan ; Douglas Kennedy ; Tomas Björk and Bent J. Christensen ; Jean-Philippe Bouchaud, Nicolas Sagna, Rama Cont, Nicole el-Karoui and Marc Potters
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