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Lognormality of Rates and Term Structure Models

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Author Info
Goldys, B., M. Musiela, and D. Sondermann
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.

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File URL: ftp://web.bgse.uni-bonn.de/pub/RePEc/bon/bonsfb/bonsfb394.pdf
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Publisher Info
Paper provided by University of Bonn, Germany in its series Discussion Paper Serie B with number 394.

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Date of creation: Nov 1996
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Handle: RePEc:bon:bonsfb:394

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Postal: Bonn Graduate School of Economics, University of Bonn, Adenauerallee 24 - 26, 53113 Bonn, Germany
Fax: +49 228 73 9221
Web page: http://www.bgse.uni-bonn.de/index.php?id=517

For technical questions regarding this item, or to correct its listing, contact: (Daniel Park).

Related research
Keywords: Term structure of interest rates lognormal volatility structure Heath Jarrow and Morton models.

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Find related papers by JEL classification:
E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Determination of Interest Rates; Term Structure of Interest Rates
G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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  1. K. Sandmann & Sondermann, D., 1993. "A Term Structure Model and the Pricing of Interest Rate Derivative," Discussion Paper Serie B 180, University of Bonn, Germany. [Downloadable!]
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This page was last updated on 2008-8-18.

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