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GRIN Verlag Statistische Verfahren für Diffusionsprozesse mit Anwendung auf stochastische Zinsmodelle der Finanzmathematik

9783638907811

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Diplomarbeit aus dem Jahr 1997 im Fachbereich Mathematik - Angewandte Mathematik, Note: 1.0, Johannes Gutenberg-Universität Mainz (Fachbereich Mathematik), 23 Quellen im Literaturverzeichnis, Sprache: Deutsch, Abstract: Statistische Verfahren für finanzmathematische Modelle sind eines der interessantesten Gebiete der Finanzmathematik. Dies liegt daran, dass die Mathematisierung der Finanzwelt immer stärker voranschreitet und mathematische Modelle exakte Inputparameter benötigen, die zuvor erst aus historischen Daten gewonnen werden müssen. Ziel dieses Buches ist es, aktuelle Schätzverfahren für bestimmte Klassen von Diffusionsprozessen detailliert vorzustellen und an Beispielen aus der Praxis zu testen. Dabei werden insbesondere die Mean-Reverting Prozesse behandelt, die Grundlage jeder Simulation der Zinsstrukturkurve sind. Ein Schwerpunk liegt dabei auf dem Vasicek Modell und dem Cox-Ingersoll-Ross Modell. Das Buch gliedert sich in drei Teile: Der erste Teil widmet sich den stochastischen Grundlagen der Diffusionsprozesse und führt in die Theorie der Zinsstrukturmodelle ein. Der zweite Teil wendet sich den Schätzverfahren für die Parameter der stochastischen Prozesse zu. Diese Verfahren ermöglichen es, die Drift und die Volatilität eines stochastischen Prozesses zu schätzen. Hier werden z.B. Maximum-Likelihood-Schätzer und Martingalschätzfunktionen vorgestellt. Im dritten und letzten Teil werden die Schätzverfahren für die Diffusionsprozesse intensiv getestet und die Tests ausgewertet. Die Tests erfolgen sowohl an simulierten als auch an historischen Datensätzen (historical backtesting). In diesem Zusammenhang werden auch die Grundlagen von QQ-Plots und der Monte-Carlo Simulation zur Erzeugung von Zeitreihen stochastischer Prozesse mittels Computerprogrammen vorgestellt.

Key Features

Used Book in Good Condition

Product Specifications

Format
paperback
Domain
Amazon UK
Release Date
01 February 2008
Listed Since
19 March 2010

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