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Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates

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Author Info

  • Miltersen, K.
  • K. Sandmann
  • D. Sondermann

Abstract

We derive a unified model which gives closed form solutions for caps and floors written on interest rates as well as puts and calls written on zero-coupon bonds. The crucial assumption is that forward rates with a compounding period that matches the contract, which we want to price, is log-normally distributed. Moreover, this assumption is shown to be consistent with the Heath-Jarrow-Morton model for a specific choice of volatility.

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File URL: http://www.wiwi.uni-bonn.de/bgsepapers/bonsfb/bonsfb308.pdf
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Bibliographic Info

Paper provided by University of Bonn, Germany in its series Discussion Paper Serie B with number 308.

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Length: pages
Date of creation: Mar 1994
Date of revision:
Handle: RePEc:bon:bonsfb:308

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Postal: Bonn Graduate School of Economics, University of Bonn, Adenauerallee 24 - 26, 53113 Bonn, Germany
Fax: +49 228 73 6884
Web page: http://www.bgse.uni-bonn.de

Related research

Keywords: Log-normal; nominal-compounding rates; Heath-Jarrow- Morton model;

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  1. 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.
  2. K. Sandmann & Sandmann, K., 1995. "The Direct Approach to Debt Option Pricing," Discussion Paper Serie B 212, University of Bonn, Germany.
  3. Rady, Sven, 1994. "The Direct Approach to Debt Option Pricing," Munich Reprints in Economics 3404, University of Munich, Department of Economics.
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