Analysen von Volatilitätssmiles für Aktien-, Index- und Währungsoptionen: Von konstanter Volatilität zur impliziten Volatilität
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Den Händlern auf Aktien- und Devisenmärkten stehen bei der Bewertung von Optionen unsichere zukünftige Zahlungsströme gegenüber, die eine grundlegende Fragestellung innerhalb der Finanzwirtschaft einnehmen. Die ersten Optionen wurden an der Chicago Board Options Exchange (CBOE) in den frühen siebziger Jahren gelistet. Zur Bewertung von europäischen Call- und Put-Optionen legen Fischer Black und Myron Scholes mit ihrem Modell im Jahre 1973 einen Meilenstein in der Finanzierungstheorie. An dieser Stelle ist auch auf die Mitwirkung von Robert C. Merton zu verweisen, der ebenfalls an der Ausarbeitung dieses Modells mitgewirkt hat, jedoch im selben Jahr eine eigenständige Publikation veröffentlichte. Aufgrund der relativ einfachen Gestaltung des Black-Scholes-Modells (BS), verbreitete sich ihre Anwendung zunehmend in der Theorie und Praxis. Seit der Einführung der ersten Optionen unterliegen die internationalen Finanz- und Kapitalmärkte einem starken Wandel, wobei in besonderen Ma en auf die Entwicklung der derivativen Hedgeinstrumente zu blicken ist. Durch die stetig wachsende Nachfrage der Unternehmen nach derivativen Instrumenten als Möglichkeit zur Risikoreduktion, wobei die Betrachtung unabhängig von den einzelnen Wirtschaftszweigen erfolgt, führen diese zu schnell wachsenden Anzahlen an verschiedenen derivativen Produkten. Dabei ist neben der Quantität der Produkte vor allem auf die Qualität abzustellen, die aufgrund ihrer zunehmenden komplexeren Struktur eine dementsprechend grö ere Herausforderung an die Bewertungsmodelle stellt. Das Optionspreismodell von Black-Scholes (Merton) zur Bewertung von europäischen Kauf- und Verkaufsoptionen über dividendenlose Aktien beinhaltet Einschränkungen, die aus den Modellannahmen resultieren. Diese führen zu verzerrter Preisbildung der Optionen, die anhand von zahlreichen empirischen Untersuchungen beobachtet wurden und deren Fokus dabei im besonderen Ma e auf die implizite Volatilität gerichtet ist. Gemä der Optionspreistheo
Zeljko Komazec, Diplom Ökonom, Studium der Wirtschaftswissenschaften an der Universität Duisburg-Essen in Duisburg. Abschluss 2009 als Diplom Ökonom.
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