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Optionsbewertung in der Praxis: Das stochastische Volatilitätsmodell nach Heston

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Mathematik im Fraunhofer-Institut

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Zusammenfassung

Optionen sind einer der wichtigsten Bausteine moderner Finanzmärkte. Die Theorie ihrer Bewertung ist eines der Vorzeigegebiete der modernen Finanzmathematik mit der Nobelpreis-gekrönten Black–Scholes-Formel als dem bekanntesten Resultat der Finanzmathematik. Allerdings ist das der Black–Scholes-Formel zugrunde liegende Modell log-normal verteilter Aktienpreise nur eine recht grobe Beschreibung für das Verhalten realer Aktienkurse. Es existieren deshalb in der Theorie eine Vielzahl von Vorschlägen mit dem Ziel der besseren Modellierung der Aktienpreisdynamik. Als ein von der Praxis akzeptierter Kompromiss zwischen theoretisch wünschenswerten Eigenschaften, hinreichend guter Modellierung und numerischer Handhabbarkeit hat sich das stochastische Volatilitätsmodell nach Heston erwiesen. Seine Eigenschaften und sein Umsetzung in der praktischen Anwendung sind Hauptgegenstand dieses Beitrags.

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Literaturverzeichnis

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Authors and Affiliations

  1. Abteilung Finanzmathematik, Fraunhofer ITWM, Fraunhofer Platz 1, 67663, Kaiserslautern, Deutschland

    Sascha Desmettre, Ralf Korn & Tilman Sayer

Authors
  1. Sascha Desmettre
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  2. Ralf Korn
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  3. Tilman Sayer
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Correspondence to Ralf Korn .

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Editors and Affiliations

  1. Techno- und Wirtschaftsmathematik (ITWM), Fraunhofer Institut für Techno- und Wirtschaftsmathematik (ITWM), Kaiserslautern, Germany

    Helmut Neunzert

  2. Techno- und Wirtschaftsmathematik (ITWM), Fraunhofer Institut für Techno- und Wirtschaftsmathematik (ITWM), Kaiserslautern, Germany

    Dieter Prätzel-Wolters

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Desmettre, S., Korn, R., Sayer, T. (2015). Optionsbewertung in der Praxis: Das stochastische Volatilitätsmodell nach Heston. In: Neunzert, H., Prätzel-Wolters, D. (eds) Mathematik im Fraunhofer-Institut. Springer Spektrum, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44877-9_10

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