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© 2006

Interest Rate Models: an Infinite Dimensional Stochastic Analysis Perspective

  • Investigates interest rate models as stochastic evolution equations in infinite dimensions

  • The three parts of the book offer an introduction to interest rates, a review of infinite dimensional stochastic analysis, and recent results in interest rate theory

  • First book to combine infinite dimensional stochastic analysis with Malliavin calculus and interest rate market models

Book

Part of the Springer Finance book series (FINANCE)

Table of contents

  1. Front Matter
    Pages I-XIV
  2. The Term Structure of Interest Rates

  3. Infinite Dimensional Stochastic Analysis

  4. Generalized Models for the Term Structure of Interest Rates

    1. Front Matter
      Pages 161-161
    2. Pages 163-194
    3. Pages 195-215
  5. Back Matter
    Pages 217-235

About this book

Introduction

Interest Rate Models: an Infinite Dimensional Stochastic Analysis Perspective studies the mathematical issues that arise in modeling the interest rate term structure. These issues are approached by casting the interest rate models as stochastic evolution equations in infinite dimensions. The book is comprised of three parts. Part I is a crash course on interest rates, including a statistical analysis of the data and an introduction to some popular interest rate models. Part II is a self-contained introduction to infinite dimensional stochastic analysis, including SDE in Hilbert spaces and Malliavin calculus. Part III presents some recent results in interest rate theory, including finite dimensional realizations of HJM models, generalized bond portfolios, and the ergodicity of HJM models.

Keywords

Infinite-Dimensional Stochastic Analysis Interest-Rate Models Malliavin Calculus calculus ergodicity modeling statistical analysis

Authors and affiliations

  1. 1.Bendheim Center for Finance Department of Operations Research and Financial EngineeringPrinceton UniversityPrincetonUSA
  2. 2.Statistical Laboratory Centre for Mathematical SciencesUniversity of CambridgeCambridgeUK

Bibliographic information

Industry Sectors
Finance, Business & Banking

Reviews

From the reviews:

"Interest rate models … is a research monograph on the theory of interest rate models in infinite dimension. … Concepts are presented in detail with appropriate examples. … It is most suitable for researchers with good background in stochastic and functional analysis … ." (Ita Cirovic Donev, MathDL-online, October, 2006)

"This book is a self-contained introduction to recent theoretical work that extends the Heath-Jarrow-Morton framework for modelling interest rates to infinite dimensions … . this is a wonderful book. The authors present some cutting-edge math in their extension of stochastic calculus to infinite dimensions. … you will find this a fascinating read." (www.riskbook.com, August, 2006)

"This book gives a rigorous, fairly complete and remarkably clear introduction to the modelling of stochastic term structure models from an infinite-dimensional point of view, and to recent research in that field. It can be used in multiple ways, as it can serve both as an introduction to the mechanics of interest rate modelling for specialists of stochastic analysis, and as an introduction to infinite-dimensional analysis for mathematicians from other fields or for practitioners. Detailed bibliographic comments are included … ." (Nicolas Privault, Mathematical Reviews, Issue 2008 a)