<div class="csl-bib-body">
<div class="csl-entry">Skorupa, M. (2018). <i>Pricing financial derivatives using Brownian motion and a Gaussian Markov alternative to fractional Brownian motion</i> [Diploma Thesis, Technische Universität Wien]. reposiTUm. https://doi.org/10.34726/hss.2018.53160</div>
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dc.identifier.uri
https://doi.org/10.34726/hss.2018.53160
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/3429
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dc.description.abstract
This thesis examines different models for pricing financial options. Instead of using Brownian motion as the underlying process, as is done in the Black-Scholes model, fractional Brownian motion is introduced and discussed. Then the Dobri-Ojeda process, a Gaussian Markov alternative, and a modified version of it will be presented as an alternative to fractional Brownian motion, based on the analysis of Conus and Wildman. In contrast to Brownian motion, fractional Brownian motion and its alternatives incorporate past dependencies, using the Hurst index. The Black-Scholes and the Conus-Wildman model will be tested on options of the S&P 500 index, where the implied volatility and the implied Hurst index are estimated. The pricing accuracy of the two models will be compared using the obtained estimators. We find that the Conus-Wildman model estimates option prices better than the Black-Scholes model, concluding that past dependencies matter and should be incorporated when pricing options.
en
dc.language
English
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dc.language.iso
en
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dc.rights.uri
http://rightsstatements.org/vocab/InC/1.0/
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dc.subject
Gauss Markov Prozess
de
dc.subject
fraktionale Brownsche Bewegung
de
dc.subject
Hurst Index
de
dc.subject
Optionspreisberechnung
de
dc.subject
implizite Volatilität
de
dc.subject
Simulation
de
dc.subject
Gaussian Markov process
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dc.subject
fractional Brownian motion
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dc.subject
Hurst index
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dc.subject
option pricing
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dc.subject
implied volatility
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dc.subject
simulation
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dc.title
Pricing financial derivatives using Brownian motion and a Gaussian Markov alternative to fractional Brownian motion
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dc.type
Thesis
en
dc.type
Hochschulschrift
de
dc.rights.license
In Copyright
en
dc.rights.license
Urheberrechtsschutz
de
dc.identifier.doi
10.34726/hss.2018.53160
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dc.contributor.affiliation
TU Wien, Österreich
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dc.rights.holder
Miriam Skorupa
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dc.publisher.place
Wien
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tuw.version
vor
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tuw.thesisinformation
Technische Universität Wien
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tuw.publication.orgunit
E105 - Institut für Stochastik und Wirtschaftsmathematik