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A Term Structure Model and the Pricing of Interest Rate Derivative


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  • K. Sandmann
  • Sondermann, D.


The paper developes a general arbitrage free model for the term structure of interest rates. The principal model is formulated in a discrete time structure. It differs substantially from the Ho--Lee-- Model (1986) and does not generate negative spot and forward rates. The results for the continuous time limit support this. The probability distribution with finite support is derived for the spot rate return. The model permits the arbitrage free valuation of bond options and interest rate options and produces dynamic portfolio strategies to duplicate these contracts.

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Bibliographic Info

Paper provided by University of Bonn, Germany in its series Discussion Paper Serie B with number 180.

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Date of creation: Mar 1993
Date of revision:
Handle: RePEc:bon:bonsfb:180

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Postal: Bonn Graduate School of Economics, University of Bonn, Adenauerallee 24 - 26, 53113 Bonn, Germany
Fax: +49 228 73 6884
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Related research

Keywords: Arbitrage; Hedging; Interest Rate; Martingale Measure; Option Pricing; Term Structure;

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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. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-92.
  3. Klaus Sandmann, 1993. "The Pricing of Options With an Uncertain Interest Rate: A Discrete-Time Approach," Mathematical Finance, Wiley Blackwell, vol. 3(2), pages 201-216.
  4. Sandmann,Klaus & Sondermann,Dieter, . "A term structure model and the pricing of interest rate options," Discussion Paper Serie B 129, University of Bonn, Germany.
  5. Sandmann,Klaus, . "An intertemporal interest rate market model: Complete markets," Discussion Paper Serie B 94, University of Bonn, Germany.
  6. Sandmann,Klaus & Sondermann,Dieter, . "Zur Bewertung von Caps und Floors," Discussion Paper Serie B 98, University of Bonn, Germany.
  7. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
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Cited by:
  1. Phelim Boyle & Ken Seng Tan & Weidong Tian, 2001. "Calibrating the Black-Derman-Toy model: some theoretical results," Applied Mathematical Finance, Taylor & Francis Journals, vol. 8(1), pages 27-48.
  2. Schlögl, Erik & Daniel Sommer, 1994. "On Short Rate Processes and Their Implications for Term Structure Movements," Discussion Paper Serie B 293, University of Bonn, Germany.
  3. D. Sondermann & K. Miltersen, 1994. "Closed Form Term Structure Derivatives in a Heath-Jarrow- Morton Model with Log-Normal Annually Compounded Interest Rates," Discussion Paper Serie B 285, University of Bonn, Germany.
  4. Goldys, B. & M. Musiela & D. Sondermann, 1996. "Lognormality of Rates and Term Structure Models," Discussion Paper Serie B 394, University of Bonn, Germany.


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