SFB 303 Discussion Paper No. B - 094
This paper is based on the work of J. M. Harrison and D. M. Kreps and makes use of the whole technique developed by them.
In contrast to their work it is intended to model a market which depends only on the interest rate structure. So
interest rate is the only source of uncertainty and dynamic force in the market. In this framework the valuation of
coupon paying debt securities is characterized in terms of martingale measures like in Harrison and Kreps. The
first model assumes that there exists a known finite number of trading dates and coupons are paid at these dates.
As coupon rates are not negative, but may be zero, it is assumed without loss of generality, that coupon
payments take place at every trading date. The second model is a continuous time generalization, that is trading
and coupon payments occur continuously. Again a martingale characterization is derived. This second part of the
paper makes use of the results obtained by J. M. Harrison and S. R. Pliska (1981,1983) and transfers them to the
interest rate market model described here. As a conclusion the market model is complete if and only if one
equivalent martingale measure exists. With the result from Yor (1978) it follows that in this model the class of
interest rate processes is limited to the Wiener and Poisson martingales.
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Creation-Date: April 1988
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