Zur Theorie des Value at Risk-minimalen Hedges

Zusammenfassung

Der vorliegende Beitrag befasst sich mit der Bestimmung der optimalen Hedge Ratio auf der Basis von Future-Kontrakten unter Zugrundelegung der Forderung, dass der Value at Risk der Hedge-Position minimiert werden soll. Unter Verwendung von Ergebnissen im Kontext von Quantilableitungen gelingt hier zunächst die Bestimmung einer allgemeinen strukturellen Lösung. Unter Ausnutzung der Eigenschaften von elliptischen Verteilungen gelingt darüber hinaus eine explizite Bestimmung der optimalen Hedge Ratio und damit eine systematische Verallgemeinerung der in der Literatur entwickelten korrespondierenden Lösung für den Normalverteilungsfall.

Abstract

The present contribution studies the problem of determining the optimal hedge ratio in the case of minimizing the value at risk of the hedge position. Using results in connection with quantile derivatives we at first are able to characterize the general solution to the problem. Using properties of the family of elliptical distribution we then are able to develop an explicit solution to the problem which generalizes the solution for the case of a (bivariate) normal distribution known from the literature.

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Correspondence to Prof. Dr. Peter Albrecht.

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Der Autor dankt dem Gutachter für wertvolle Hinweise und Anregungen

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Albrecht, P. Zur Theorie des Value at Risk-minimalen Hedges. Schmalenbachs Z betriebswirtsch Forsch 63, 2–18 (2011). https://doi.org/10.1007/BF03372842

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JEL-Classification

  • G11
  • G 32

Keywords

  • Elliptical Distributions
  • Hedge Ratio
  • Linear Prediction
  • Quantile Derivative

Schlüsselwörter

  • Elliptische Verteilungen
  • Hedge Ratio
  • Lineare Vorhersage
  • Quantilableitung