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.
Creation-Date: January 1989
Unfortunately this paper is not available online. Please contact us to order a hardcopy.

SFB 303 Homepage

21.10.1999, Webmaster