HJM: A unified approach to dynamic models for fixed income, credit and equity markets

Research output: Chapter in Book/Report/Conference proceedingChapter

6 Scopus citations

Abstract

The purpose of this paper is to highlight some of the key elements of the HJM approach as originally introduced in the framework of fixed income market models, to explain how the very same philosophy was implemented in the case of credit portfolio derivatives and to show how it can be extended to and used in the case of equity market models. In each case we show how the HJM approach naturally yields a consistency condition and a no-arbitrage condition in the spirit of the original work of Heath, Jarrow and Morton. Even though the actual computations and the derivation of the drift condition in the case of equity models seems to be new, the paper is intended as a survey of existing results, and as such, it is mostly pedagogical in nature.

Original languageEnglish (US)
Title of host publicationParis-Princeton Lectures on Mathematical Finance 2004
PublisherSpringer Verlag
Pages1-50
Number of pages50
ISBN (Print)3540733264, 9783540733263
DOIs
StatePublished - Jan 1 2007

Publication series

NameLecture Notes in Mathematics
Volume1919
ISSN (Print)0075-8434

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Keywords

  • Arbitrage-free term structure dynamics
  • Health-Jarrow-Morton theory
  • Implied volatilty surface
  • Local volatility surface
  • Market models

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  • Cite this

    Carmona, R. A. (2007). HJM: A unified approach to dynamic models for fixed income, credit and equity markets. In Paris-Princeton Lectures on Mathematical Finance 2004 (pp. 1-50). (Lecture Notes in Mathematics; Vol. 1919). Springer Verlag. https://doi.org/10.1007/978-3-540-73327-0_1