Implied savings accounts are unique

Martin Schweizer (), Christophe Stricker () and Frank DÃberlein ()
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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

Finance and Stochastics, 2000, vol. 4, issue 4, 442 pages

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.

Keywords: term structure models; implied savings account; Doob-Meyer decomposition; semimartingales; multiplicative decomposition (search for similar items in EconPapers)
JEL-codes: G10 (search for similar items in EconPapers)
Date: 2000-08-11
Note: received: June 1999; final version received: November 1999
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