SENSITIVITY WITH RESPECT TO THE YIELD CURVE: DURATION IN A STOCHASTIC SETTING

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 deriva...

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Main Authors: Kettler, Paul C, Proske, Frank, Rubtsov, Mark
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Proske, Frank
Rubtsov, Mark
description 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 delta hedges) of portfolios of interest-rate-sensitive securities with respect to the fluctuation of the whole yield surface.
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title SENSITIVITY WITH RESPECT TO THE YIELD CURVE: DURATION IN A STOCHASTIC SETTING
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