The generalization of the Geske-formula for compound options to stochastic interest rates is not trivial – a note

This note refers to the paper by German et al., in which an extension of the Geske-formula for compound options to the case of stochastic interest rates is proposed. We show that such an extension is not possible in general. However, we point out modifications of Geske's original problem in which closed formulas can still be obtained under stochastic interest rates. In particular we consider the case of an option on a future-style option. Moreover, we sketch a numerical solution to Geske's original problem when interest rates are random.