SFB 303 Discussion Paper No. B - 129

Author: Sandmann, Klaus, and Dieter Sondermann
Title: A Term Structure Model and the Pricing of Interest Rate Options
Abstract: The forecast of future interest rates is a serious problem and the risk involved with the interest rate evaluation has become of increasing importance for investors. So it is natural to think about an insurance against this risk. Closely related to option contracts over stocks are recently introduced interest rate options which offer the possibility of protection against unfavorable interest rate movements. Examples of such interest rate based contracts are caps and floors. In order to prevent arbitrage opportunities, it is necessary to model the whole term structure. A first solution to this problem in a binomial model is given by T. Ho and Sang-Bin Lee (1986). Unfortunately their model allows for negative interest rates. In the present paper we propose a binomial model of the term structure, which differs from the Ho-Lee-Model. Our risk measure is the volatility of the spot rate and not of the return. Furthermore, negative spot rates are not generated within the model. The model allows for the arbitrage free valuation of interest rate options and produces dynamic hedge strategies to duplicate these options, where it is possible to choose from several equivalent strategies. The paper is organized as follows. In the first section we give a definition of cap and floor contracts and show some properties resulting from the no arbitrage conditions. The term structure model is given in section 2. The third section looks at the pricing of interest rate options and the possible hedge strategies. Some simulation and a discussion of the model parameters are given in section 4.
Creation-Date: December 1989
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