Transformation of Heath-Jarrow-Morton Models to Markovian Systems

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Transformation of Heath-Jarrow-Morton Models to Markovian Systems

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Ram Bhar (School of Banking and Finance, University of New South Wales)
Carl Chiarella () (School of Finance and Economics, University of Technology, Sydney)

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Carl Chiarella

Abstract

A class of volatility functions for the forward rate process is considered, which allows the bond price dynamics in the Heath-Jarrow-Morton (HJM) framework to be reduced to a finite dimensional Markovian system. The use of this Markovian system in estimation of parameters of the volatility function via use of the Kalman filter is discussed. Further, the Markovian system allows the link to be drawn between the HJM and the Vasicek/Cox-Ingersoll-Ross (CIR) frameworks for modelling the term structure of interest rates.

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Paper provided by School of Finance and Economics, University of Technology, Sydney in its series Working Paper Series with number 53.

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Length: 31 pages
Date of creation: 01 Dec 1995
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Handle: RePEc:uts:wpaper:53

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Ram Bhar & Carl Chiarella, 1995. "The Estimation of the Heath-Jarrow-Morton Model by Use of Kalman Filtering Techniques," Working Paper Series 54, School of Finance and Economics, University of Technology, Sydney. [Downloadable!]
Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January. [Downloadable!] (restricted)
Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March. [Downloadable!] (restricted)
Amin, Kaushik I. & Morton, Andrew J., 1994. "Implied volatility functions in arbitrage-free term structure models," Journal of Financial Economics, Elsevier, vol. 35(2), pages 141-180, April. [Downloadable!] (restricted)
Ho, Thomas S Y & Lee, Sang-bin, 1986. " Term Structure Movements and Pricing Interest Rate Contingent Claims," Journal of Finance, American Finance Association, vol. 41(5), pages 1011-29, December. [Downloadable!] (restricted)

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