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GARCH(1,1) models

Ruprecht-Karls-Universit at HeidelbergFakult at f ur Mathematik und InformatikBachelorarbeitzur Erlangung des akademischen GradesBachelor of Science (B. Sc.) garch (1,1) modelsvorgelegt vonBrandon Williams15. Juli 2011 Betreuung: Prof. Dr. Rainer DahlhausAbstraktIn dieser Bachelorarbeit werden garch (1,1)-Modelle zur Analyse finanzieller Zeitreihen unter-sucht. Dabei werden zuerst hinreichende und notwendige Bedingungen daf ur gegeben, dass solcheProzesse uberhaupt station ar werden k onnen. Danach werden asymptotische Ergebnisse uber rel-evante Sch atzer hergeleitet und parametrische Tests entwickelt. Die Methoden werden am Endedurch ein Datenbeispiel this thesis, garch (1,1)- models for the analysis of financial time series are investigated.

and this is one of the well known \stylized facts" of mathematical nance. The presence of heteroskedasticity is ignored in some nancial models such as the Black-Scholes model, which is widely used to determine the fair pricing of European-style options.

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