SFB 303 Discussion Paper No. B - 394

Author: Goldys, B., M. Musiela, and D. Sondermann
Title: Lognormality of Rates and Term Structure Models
Abstract: A term structure model with lognormal type volatility structure is proposed. The Heath, Jarrow and Morton (HJM) framework, coupled with the theory of stochastic evolution equations in infinite dimensions, is used to show that the resulting rates are well defined (they do not explode) and remain positive. They are bounded from below and above by lognormal processes. The model can be used to price and hedge caps, swaptions and other interest rate and currency derivatives including the Eurodollar futures contract, which requires integrability of one over zero coupon bond. This extends results obtained by Sandmann and Sondermann (1993), (1994) for Markovian lognormal short rates to (non-Markovian) lognormal forward rates.
Keywords: Term structure of interest rates, lognormal volatility structure, Heath, Jarrow and Morton models.
JEL-Classification-Number: E43, G13
Creation-Date: November 1996
URL: ../1996/b/bonnsfb394.pdf

SFB 303 Homepage

14.04.1998, Webmaster