Sensitivity with Respect to the Yield Curve: Duration in a Stochastic Setting

Paul C. Kettler (), Frank Proske () and Mark Rubtsov ()
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Paul C. Kettler: University of Oslo, CMA, Department of Mathematics
Frank Proske: University of Oslo, CMA, Department of Mathematics
Mark Rubtsov: University of Oslo, CMA, Department of Mathematics

A chapter in Inspired by Finance, 2014, pp 363-385 from Springer

Abstract: Abstract Bond duration in its basic deterministic meaning form is a concept well understood. Its meaning in the context of a yield curve on a stochastic path is less well developed. In this paper we extend the basic idea to a stochastic setting. More precisely, we introduce the concept of stochastic duration as a Malliavin derivative in the direction of a stochastic yield surface modeled by the Musiela equation. Further, using this concept we also propose a mathematical framework for the construction of immunization strategies (or delta hedges) of portfolios of interest rate securities with respect to the fluctuation of the whole yield surface.

Keywords: Bond duration; Malliavin derivative; Yield surface; Immunization strategies; Delta hedges; 91G30; 60H07; 91B02 (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-02069-3_17

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DOI: 10.1007/978-3-319-02069-3_17

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