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

In: Inspired by Finance

Author

Listed:
  • 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)

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.

Suggested Citation

  • Paul C. Kettler & Frank Proske & Mark Rubtsov, 2014. "Sensitivity with Respect to the Yield Curve: Duration in a Stochastic Setting," Springer Books, in: Yuri Kabanov & Marek Rutkowski & Thaleia Zariphopoulou (ed.), Inspired by Finance, edition 127, pages 363-385, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-02069-3_17
    DOI: 10.1007/978-3-319-02069-3_17
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