# SFB 303 Discussion Paper No. B - 114

**Author**: Sandmann, Klaus

**Title**: The Pricing of Options with an Uncertain Interest Rate: A Discrete Approach

**Abstract**: The aim of the paper is to look at the pricing of European type options under the assumption of a stochastic
interest rate in a discrete time context. Therefore, the well-known binomial approach for the description of the
stock price movements is combined with the term structure model of Sandmann and Sondermann (1988).
Basically two problems are connected with this approach. First, it is necessary to formulate a relationship
between stock price movements and interest rate movements. It turns out that correlation is not enough. Second,
it is no longer possible to set up a self-financing strategy to duplicate the option. To solve the latter problem, the
idea of risk-minimizing strategies of H. Föllmer and D. Sondermann (1986) is used. So the paper gives a hint
that the situation may become complicated in a very basic formulation, if one allows the term structure to be
stochastic.

The paper is organized as follows: Section 1 contains a brief description of the binomial model. The
term structure model of Sandmann and Sondermann is briefly reviewed in Section 2. The combination of the two
models is given in Section 3. Finally, Section 4 deals with the risk-minimizing strategy in order to approximate
the option impact.

**Keywords**:

**JEL-Classification-Number**:

**Creation-Date**: January 1989

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