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Implied savings accounts are unique

Author

Listed:
  • 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.

Suggested Citation

  • Martin Schweizer & Christophe Stricker & Frank DÃberlein, 2000. "Implied savings accounts are unique," Finance and Stochastics, Springer, vol. 4(4), pages 431-442.
    • Handle: RePEc:spr:finsto:v:4:y:2000:i:4:p:431-442
    Note: received: June 1999; final version received: November 1999
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    Citations

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    Cited by:

    1. Likuan Qin & Vadim Linetsky, 2014. "Positive Eigenfunctions of Markovian Pricing Operators: Hansen-Scheinkman Factorization, Ross Recovery and Long-Term Pricing," Papers 1411.3075, arXiv.org, revised Sep 2015.
    2. Likuan Qin & Vadim Linetsky, 2014. "Long Term Risk: A Martingale Approach," Papers 1411.3078, arXiv.org, revised Oct 2016.
    3. Likuan Qin & Vadim Linetsky, 2016. "Positive Eigenfunctions of Markovian Pricing Operators: Hansen-Scheinkman Factorization, Ross Recovery, and Long-Term Pricing," Operations Research, INFORMS, vol. 64(1), pages 99-117, February.

    More about this item

    Keywords

    term structure models; implied savings account; Doob-Meyer decomposition; semimartingales; multiplicative decomposition;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

    Statistics

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