Exotic Option Pricing in Stochastic Volatility Levy Models and with Fractional Brownian Motion

Graf, Ferdinand

Exotic Option Pricing in Stochastic Volatility Levy Models and with Fractional Brownian Motion

Dateien

Graf_Dipl.pdfGröße: 6.23 MBDownloads: 842

Datum

2007

Open Access-Veröffentlichung

Open Access Green

Sammlungen

Wirtschaftswissenschaften

Publikationstyp

Masterarbeit/Diplomarbeit

Publikationsstatus

Published

Zusammenfassung

The paper Exotic Option Pricing in Stochastic Volatility Levy Models and with Fractional Brownian Motion aims on extending the restrictive Black-Scholes model by allowing volatility to evolve randomly. These models are used to price exotic derivatives and certificates. The first stochastic volatility model is the Heston model. In order to capture jumps in volatility and stock evolution, Levy processes and Ornstein-Uhlenbeck processes are under discussion. Using the convenient features of Levy processes, a stochastic volatility stock evolution model, where volatility is driven by a Levy process and volatility evolution and stock evolution are linked, is introduced.
This model is named after Barndorff-Nielsen and Shephard (BNS for short). However, the BNS model does not include the long memory behavior of volatility. This justifies a discussion about the fractional Brownian motion, the most important stochastic process to model long memory. Finally, the different models are calibrated by fitting prices of observed European options and compared when bonus certificates and express certificates are valued.

Fachgebiet (DDC)

330 Wirtschaft

Schlagwörter

stochastic volatility, exotic options, bonus certificates, express certificates, barrier options, Levy process, Ornstein-Uhlenbeck process, BNS

Zitieren

ISO 690

GRAF, Ferdinand, 2007. Exotic Option Pricing in Stochastic Volatility Levy Models and with Fractional Brownian Motion [Master thesis]

BibTex

@mastersthesis{Graf2007Exoti-11839,
  year={2007},
  title={Exotic Option Pricing in Stochastic Volatility Levy Models and with Fractional Brownian Motion},
  author={Graf, Ferdinand}
}

RDF

<rdf:RDF
    xmlns:dcterms="http://purl.org/dc/terms/"
    xmlns:dc="http://purl.org/dc/elements/1.1/"
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:bibo="http://purl.org/ontology/bibo/"
    xmlns:dspace="http://digital-repositories.org/ontologies/dspace/0.1.0#"
    xmlns:foaf="http://xmlns.com/foaf/0.1/"
    xmlns:void="http://rdfs.org/ns/void#"
    xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > 
  <rdf:Description rdf:about="https://kops.uni-konstanz.de/server/rdf/resource/123456789/11839">
    <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/46"/>
    <dcterms:rights rdf:resource="http://creativecommons.org/licenses/by-nc-nd/2.0/"/>
    <dc:contributor>Graf, Ferdinand</dc:contributor>
    <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/46"/>
    <dc:format>application/pdf</dc:format>
    <dcterms:hasPart rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/11839/1/Graf_Dipl.pdf"/>
    <bibo:uri rdf:resource="http://kops.uni-konstanz.de/handle/123456789/11839"/>
    <dc:language>eng</dc:language>
    <dspace:hasBitstream rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/11839/1/Graf_Dipl.pdf"/>
    <dcterms:abstract xml:lang="eng">The paper  Exotic Option Pricing in Stochastic Volatility Levy Models and with Fractional Brownian Motion  aims on extending the restrictive Black-Scholes model by allowing volatility to evolve randomly. These models are used to price exotic derivatives and certificates. The first stochastic volatility model is the Heston model. In order to capture jumps in volatility and stock evolution, Levy processes and Ornstein-Uhlenbeck processes are under discussion. Using the convenient features of Levy processes, a stochastic volatility stock evolution model, where volatility is driven by a Levy process and volatility evolution and stock evolution are linked, is introduced.&lt;br /&gt;This model is named after Barndorff-Nielsen and Shephard (BNS for short). However, the BNS model does not include the long memory behavior of volatility. This justifies a discussion about the fractional Brownian motion, the most important stochastic process to model long memory. Finally, the different models are calibrated by fitting prices of observed European options and compared when bonus certificates and express certificates are valued.</dcterms:abstract>
    <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2011-03-25T09:40:36Z</dc:date>
    <dcterms:title>Exotic Option Pricing in Stochastic Volatility Levy Models and with Fractional Brownian Motion</dcterms:title>
    <dc:creator>Graf, Ferdinand</dc:creator>
    <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2011-03-25T09:40:36Z</dcterms:available>
    <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
    <dc:rights>Attribution-NonCommercial-NoDerivs 2.0 Generic</dc:rights>
    <foaf:homepage rdf:resource="http://localhost:8080/"/>
    <dcterms:issued>2007</dcterms:issued>
  </rdf:Description>
</rdf:RDF>

Universitätsbibliographie

Ja