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A Preference Free Partial Differential Equation for the Term Stucture of Interest Rates

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Abstract

The objectives of this paper are twofold: 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.

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File URL: http://www.finance.uts.edu.au/research/wpapers/wp63.pdf
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Bibliographic Info

Paper provided by Finance Discipline Group, UTS Business School, University of Technology, Sydney in its series Working Paper Series with number 63.

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Date of creation: 01 May 1996
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Publication status: Published as: Chiarella, C. and El-Hassan, N., 1996, "A Preference Free Partial Differential Equation for the Term Structure of Interest Rates", Financial Engineering and the Japanese Markets, 3(3), 217-238.
Handle: RePEc:uts:wpaper:63

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Cited by:
  1. Carl Chiarella & Nadima El-Hassan, 1999. "Pricing American Interest Rate Options in a Heath-Jarrow-Morton Framework Using Method of Lines," Research Paper Series 12, Quantitative Finance Research Centre, University of Technology, Sydney.
  2. Christina Nikitopoulos-Sklibosios, 2005. "A Class of Markovian Models for the Term Structure of Interest Rates Under Jump-Diffusions," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 6.
  3. Ramaprasad Bhar & Carl Chiarella, 1997. "Interest rate futures: estimation of volatility parameters in an arbitrage-free framework," Applied Mathematical Finance, Taylor & Francis Journals, vol. 4(4), pages 181-199.
  4. Carl Chiarella & Christina Sklibosios, 2003. "A Class of Jump-Diffusion Bond Pricing Models within the HJM Framework," Asia-Pacific Financial Markets, Springer, vol. 10(2), pages 87-127, September.
  5. Ramaprasad Bhar, 2010. "Stochastic Filtering With Applications In Finance:," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 7736.

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