Consistency Problems for Heath-Jarrow-Morton Interest Rate Models

  • Authors
  • Damir Filipović

Part of the Lecture Notes in Mathematics book series (LNM, volume 1760)

Table of contents

  1. Front Matter
    Pages N2-VIII
  2. Damir Filipović
    Pages 1-11
  3. Damir Filipović
    Pages 13-27
  4. Damir Filipović
    Pages 29-56
  5. Damir Filipović
    Pages 57-73
  6. Damir Filipović
    Pages 75-94
  7. Damir Filipović
    Pages 95-111
  8. Damir Filipović
    Pages 113-125
  9. Damir Filipović
    Pages 127-128
  10. Damir Filipović
    Pages 129-131
  11. Damir Filipović
    Pages 133-134
  12. Back Matter
    Pages 135-137

About this book

Introduction

The book is written for a reader with knowledge in mathematical finance (in particular interest rate theory) and elementary stochastic analysis, such as provided by Revuz and Yor (Continuous Martingales and Brownian Motion, Springer 1991). It gives a short introduction both to interest rate theory and to stochastic equations in infinite dimension. The main topic is the Heath-Jarrow-Morton (HJM) methodology for the modelling of interest rates. Experts in SDE in infinite dimension with interest in applications will find here the rigorous derivation of the popular "Musiela equation" (referred to in the book as HJMM equation). The convenient interpretation of the classical HJM set-up (with all the no-arbitrage considerations) within the semigroup framework of Da Prato and Zabczyk (Stochastic Equations in Infinite Dimensions) is provided. One of the principal objectives of the author is the characterization of finite-dimensional invariant manifolds, an issue that turns out to be vital for applications. Finally, general stochastic viability and invariance results, which can (and hopefully will) be applied directly to other fields, are described.

Keywords

Measure Volatility bond markets interest rates invariant models mathematical finance stochastic differential equations term structure

Bibliographic information

  • DOI https://doi.org/10.1007/b76888
  • Copyright Information Springer-Verlag Berlin Heidelberg 2001
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-41493-3
  • Online ISBN 978-3-540-44548-7
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book