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

Part of: Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Rüdiger Frey  and
Daniel Sommer
Rüdiger Frey*
Affiliation:
Eidgenössische Technische Hochschule Zürich
Daniel Sommer*
Affiliation:
Universität Bonn
*
∗Postal address: Dept. of Mathematics, ETH Zurich, ETH Zentrum, CH-8092 Zurich, Switzerland. E-mail address: frey@math.ethz.ch
∗∗Postal address: Statistische Abteilung, Institut für Wirtschafts- und Gesellschaftswissenschaften, Rechts- und Staatswissenschaftliche Fakultät, Universität Bonn, Adenauerallee 24–42, D-53113 Bonn.
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Abstract

This note refers to the paper by Geman, El-Karoui and Rochet (1995), 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.

Keywords

Compound optionsstochastic interest ratesfutures-style optionschange of numeraire technique

MSC classification

Secondary: 60G35: Signal detection and filtering
Type
Short Communications
Information
Journal of Applied Probability , Volume 35 , Issue 2 , June 1998 , pp. 501 - 509
Copyright
Copyright © Applied Probability Trust 1998 

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