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A Markovian Framework in Multi-Factor Heath-Jarrow-Morton Models

Published online by Cambridge University Press:  06 April 2009

Koji Inui  and
Masaaki Kijima
Koji Inui
Affiliation:
Financial Research Department, NLI Research Institute, 1–1–1 Yuraku-cho, Chiyoda-ku, Tokyo 100–0006, Japan
Masaaki Kijima
Affiliation:
Faculty of Economics, Tokyo Metropolitan University, 1–1 Minami-Ohsawa, Hachiohji, Tokyo 192–0397, Japan.
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Abstract

We consider the general n-factor Heath, Jarrow, and Morton model (1992) and provide a sufficient condition on the volatility structure for the spot rate process to be Markovian with 2n state variables. The price of a discount bond is also Markovian with the same state variables and, hence, claims against the term structure can be efficiently priced using standard simulation techniques. Our results extend earlier works such as Ritchken and Sankarasubramanian (1995) where the one-factor model is treated, and Carverhill (1994), where the volatility structure is non-random. Numerical experiments show that our model can explain the volatility smile observed in the interest rate options market and also overcome the biases noted by Flesaker (1993).

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 33 , Issue 3 , September 1998 , pp. 423 - 440
Copyright
Copyright © School of Business Administration, University of Washington 1998

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