Financial Engineering and the Japanese Markets

, Volume 3, Issue 3, pp 217–238 | Cite as

A preference free partial differential equation for the term structure of interest rates

  • Carl Chiarella
  • Nadima El-Hassan


The objectives of this paper are two-fold: the first is the reconciliation of the differences between the Vasicek and the Heath-Jarrow-Morton approaches to the modelling of term structure of interest rates. We demonstrate that under certain (not empirically unreasonable) assumptions prices of interest-rate sensitive claims within the Heath-Jarrow-Morton framework can be expressed as a partial differential equation which both is preference-free and matches the currently observed yield curve. This partial differential equation is shown to be equivalent to the extended Vasicek model of Hull and White. The second is the pricing of interest rate claims in this framework. The preference free partial differential equation that we obtain has the added advantage that it allows us to bring to bear on the problem of evaluating American style contingent claims in a stochastic interest rate environment the various numerical techniques for solving free boundary value problems which have been developed in recent years such as the method of lines.

Key words

Heath-Jarrow-Morton term structure of interest rates preference-free partial differential equation American options free boundary value problems method of lines 


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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Carl Chiarella
    • 1
  • Nadima El-Hassan
    • 1
  1. 1.School of Finance and EconomicsUniversity of TechnologySydneyAustralia

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