Inspired by Finance 2014
DOI: 10.1007/978-3-319-02069-3_17
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Sensitivity with Respect to the Yield Curve: Duration in a Stochastic Setting

Abstract: Abstract. Bond duration in its basic deterministic form is a concept well understood. Its meaning in the context of a yield curve on a stochastic path is less well developed. 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… Show more

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Cited by 1 publication
(4 citation statements)
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“…In the paper [4] where the concept of duration under discussion was originally introduced, the emphasis was on the theoretical construction which did not straightforwardly lead to numerical results. We have here adapted the model to yield a computationally tractable numerical algorithm.…”
Section: Resultsmentioning
confidence: 99%
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“…In the paper [4] where the concept of duration under discussion was originally introduced, the emphasis was on the theoretical construction which did not straightforwardly lead to numerical results. We have here adapted the model to yield a computationally tractable numerical algorithm.…”
Section: Resultsmentioning
confidence: 99%
“…[3]), are therefore not suitable for complex hedging portfolios of bonds, since the portfolio weights with respect to the hedged positions usually depend on the whole term structure of interest rates and hence are time-dependent functionals of the (stochastic) yield surface. In order to overcome this problem, one could use the concept of stochastic duration in [4] to measure the yield surface sensitivity of bond portfolios. Here the stochastic duration, which can be considered a generalization of the classical duration of Macaulay, is defined as a Malliavin derivative in the direction of the (centered) forward curve , 0…”
Section: Introductionmentioning
confidence: 99%
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