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Closed Form Term Structure Derivatives in a Heath-Jarrow- Morton Model with Log-Normal Annually Compounded Interest Rates

  • D. Sondermann
  • K. Miltersen
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    Starting with observable annually compounded forward rates we derive a term structure model of interest rates. The model relies upon the assumption that a specific set of annually compounded forward rates is log-normally distributed. We derive solutions for interest rate caps and floors as well as puts and calls written on zero-coupon bonds. In particular, for caplets with payment periods of same length as the compounding period (in our paper we have chosen one year, but it could be as well three or six months with quarterly or biannual compounding) we obtain the same Black formula as often used by market practioners, however, without making the unrealistic assumption that forward rates are independent of the accummulation process. Moreover, the log-normal 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/bonsfb285.ps
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    Paper provided by University of Bonn, Germany in its series Discussion Paper Serie B with number 285.

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    Date of creation: Aug 1994
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    Handle: RePEc:bon:bonsfb:285
    Contact details of provider: 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

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    1. Rady, Sven, 1994. "The Direct Approach to Debt Option Pricing," Munich Reprints in Economics 3404, University of Munich, Department of Economics.
    2. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
    3. K. Sandmann & Sandmann, K., 1995. "The Direct Approach to Debt Option Pricing," Discussion Paper Serie B 212, University of Bonn, Germany.
    4. 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.
    5. Chan, K C, et al, 1992. " An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," Journal of Finance, American Finance Association, vol. 47(3), pages 1209-27, July.
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