Martin Schweizer () (Technische UniversitÄt Berlin, Fachbereich Mathematik, MA 7-4, Strañe des 17. Juni 136, D-10623 Berlin, Germany) Christophe Stricker () (Laboratoire de MathÊmatiques, UniversitÊ de Franche-ComtÊ, UMR CNRS 6623, 16 Route de Gray, F-25030 BesanÚon Cedex, France Manuscript) Frank DÃberlein () (Deutsche Bank AG, Global Markets, Groñe Gallusstrañe 10-14, D-60311 Frankfurt am Main, Germany)
Abstract
An implied savings account for a given term structure model is a strictly positive predictable process A of finite variation such that zero coupon bond prices are given by $B(t,T)=E^Q\left[{A_t \over A_T} \Big| {\cal F}_t \right]$ for some Q equivalent to the original probability measure. We prove that if $(A^\prime,Q^\prime)$ is another pair with the same properties, then A and $A^\prime$ are indistinguishable. This extends a result given by Musiela and Rutkowski (1997a) who considered the case of a Brownian filtration, and fills a gap in their arguments.
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