Chapter

Heath‐Jarrow‐Morton Models

Claus Munk

in Fixed Income Modelling

Published in print June 2011 | ISBN: 9780199575084
Published online September 2011 | e-ISBN: 9780191728648 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199575084.003.0010
Heath‐Jarrow‐Morton Models

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Instead of calibrating a simple diffusion model to match the observed yield curve, a more natural modelling approach is to start from the observed yield curve and then modelling its possible future evolution. This is the approach taken by the so-called Heath–Jarrow–Morton (HJM) models studied in this chapter. The HJM models specify the dynamics of all forward interest rates and a key result is a link between the drift and volatilities of the forward rates. The main characteristics, advantages, and drawbacks of this approach are presented as well as several specific HJM models including highly tractable Gaussian models. The relationship between HJM models and the diffusion models discussed in previous chapters is discussed.

Keywords: Heath-Jarrow-Morton models; forward rate dynamics; drift restriction; extended Vasicek; extended Cox–Ingersoll–Ross; diffusion representation; Gaussian model

Chapter.  11368 words. 

Subjects: Financial Markets

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