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[{"key": "dc.contributor.advisor", "value": "Geiss, Stefan", "language": null, "element": "contributor", "qualifier": "advisor", "schema": "dc"}, {"key": "dc.contributor.author", "value": "Puustinen, Timo", "language": null, "element": "contributor", "qualifier": "author", "schema": "dc"}, {"key": "dc.date.accessioned", "value": "2016-12-18T19:36:26Z", "language": null, "element": "date", "qualifier": "accessioned", "schema": "dc"}, {"key": "dc.date.available", "value": "2016-12-18T19:36:26Z", "language": null, "element": "date", "qualifier": "available", "schema": "dc"}, {"key": "dc.date.issued", "value": "2016", "language": null, "element": "date", "qualifier": "issued", "schema": "dc"}, {"key": "dc.identifier.other", "value": "oai:jykdok.linneanet.fi:1644658", "language": null, "element": "identifier", "qualifier": "other", "schema": "dc"}, {"key": "dc.identifier.uri", "value": "https://jyx.jyu.fi/handle/123456789/52406", "language": null, "element": "identifier", "qualifier": "uri", "schema": "dc"}, {"key": "dc.description.abstract", "value": "T\u00e4ss\u00e4 tutkielmassa esitell\u00e4\u00e4n tapa laskea diskreetti approksimaatio option deltalle. Approksimaatio saadaan diskreetin Malliavin-laskennan avulla ja t\u00e4t\u00e4 varten m\u00e4\u00e4ritell\u00e4\u00e4n Malliavin-derivaatta sek\u00e4 Skorohod-integraali sopivaan diskreettiin todenn\u00e4k\u00f6isyysavaruuteen. Tavoitteena on laskea eurooppalaisen osto-option ja bin\u00e4\u00e4rioption deltat.\n\nEnsimm\u00e4isess\u00e4 luvussa esitell\u00e4\u00e4n oleellisimpia m\u00e4\u00e4ritelmi\u00e4, esimerkkej\u00e4 ja aputuloksia, joita tarvitaan esitiedoiksi my\u00f6hempi\u00e4 lukuja varten. Luvun m\u00e4\u00e4ritelmiin ja aputuloksiin ei kuitenkaan syvennyt\u00e4 sen enemp\u00e4\u00e4. Heti toisen luvun alussa m\u00e4\u00e4ritell\u00e4\u00e4n todenn\u00e4k\u00f6isyysavaruus diskreetti\u00e4 satunnaisk\u00e4vely\u00e4 varten. Satunnaisk\u00e4vely\u00e4 k\u00e4ytet\u00e4\u00e4n diskreetiss\u00e4 optionhinnoittelumallissa Brownin liikkeen vastineena, siis mallinnettaessa option kohde-etuuden hintaa. Toisessa luvussa k\u00e4sitell\u00e4\u00e4n my\u00f6s diskreetti\u00e4 Malliavin-laskentaa ja m\u00e4\u00e4ritell\u00e4\u00e4n kaksi oleellista k\u00e4sitett\u00e4: Malliavin-derivaatta ja diskreetti Skorohod-integraali. Malliavin-derivaatan m\u00e4\u00e4ritelm\u00e4n yhteydess\u00e4 esitet\u00e4\u00e4n tulokset, joiden nojalla diskreetti Malliavin-derivaatta yhdistyy tietyin oletuksin tavalliseen derivaattaan. Vastaava tulos esitet\u00e4\u00e4n my\u00f6s yhdistetyille funktioille. Toisen luvun lopussa m\u00e4\u00e4ritell\u00e4\u00e4n Skorohod-integraali ja todistetaan diskreetin Malliavin-laskennan osittaisintegrointikaava.\n\nKolmas ja viimeinen luku k\u00e4sittelee binomipuumallia ja option deltan laskemista diskreetin Malliavin-laskennan avulla. Luku rakentuu siten, ett\u00e4 ensin m\u00e4\u00e4ritell\u00e4\u00e4n binomipuumalli, jolla mallinnetaan option kohde-etuuden hintaa. Sen avulla saadaan diskreetit approksimaatiot Black-Scholes -mallin mukaiselle option hinnalle ja option deltalle. T\u00e4m\u00e4n j\u00e4lkeen option deltalle johdetaan muoto tilanteessa, jossa option tuottofunktio t\u00e4ytt\u00e4\u00e4 tietyt oletukset. Erityisesti tuottofunktion tulee olla rajoitettu, jatkuva ja derivoituva. Edelt\u00e4vi\u00e4 oletuksia voidaan kuitenkin lievent\u00e4\u00e4. Option tuottofunktiolla voi olla pisteit\u00e4, joissa se ei ole derivoituva tai edes jatkuva. Viimeisess\u00e4 ja t\u00e4rkeimm\u00e4ss\u00e4 lauseessa lasketaan delta optiolle, jolla on \u00e4\u00e4rellinen m\u00e4\u00e4r\u00e4 ongelmapisteit\u00e4 ja jota voidaan approksimoida kaksi kertaa jatkuvasti derivoituvalla funktiolla kaikkien ongelmapisteiden ymp\u00e4rist\u00f6iss\u00e4.", "language": "fi", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted using Plone Publishing form by Timo Puustinen (tipepuus) on 2016-12-18 19:36:26.305907. Form: Pro gradu -lomake (https://kirjasto.jyu.fi/julkaisut/julkaisulomakkeet/pro-gradu-lomake). JyX data: [jyx_publishing-allowed (fi) =True]", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted by jyx lomake-julkaisija (jyx-julkaisija.group@korppi.jyu.fi) on 2016-12-18T19:36:26Z\nNo. of bitstreams: 2\nURN:NBN:fi:jyu-201612185147.pdf: 439229 bytes, checksum: 57a6a71b35e895c5038b51f8a24e486c (MD5)\nlicense.html: 4821 bytes, checksum: e4ec3c9c5d4b8607e0caa24a244f7961 (MD5)", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Made available in DSpace on 2016-12-18T19:36:26Z (GMT). No. of bitstreams: 2\nURN:NBN:fi:jyu-201612185147.pdf: 439229 bytes, checksum: 57a6a71b35e895c5038b51f8a24e486c (MD5)\nlicense.html: 4821 bytes, checksum: e4ec3c9c5d4b8607e0caa24a244f7961 (MD5)\n Previous issue date: 2016", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.format.extent", "value": "1 verkkoaineisto (45 sivua)", "language": null, "element": "format", "qualifier": "extent", "schema": "dc"}, {"key": "dc.format.mimetype", "value": "application/pdf", "language": null, "element": "format", "qualifier": "mimetype", "schema": "dc"}, {"key": "dc.language.iso", "value": "fin", "language": null, "element": "language", "qualifier": "iso", "schema": "dc"}, {"key": "dc.rights", "value": "In Copyright", "language": "en", "element": "rights", "qualifier": null, "schema": "dc"}, {"key": "dc.subject.other", "value": "Malliavin-laskenta", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "binomipuumalli", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "option delta", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.title", "value": "Option deltan laskeminen diskreetin Malliavin-laskennan avulla", "language": null, "element": "title", "qualifier": null, "schema": "dc"}, {"key": "dc.type", "value": "master thesis", "language": null, "element": "type", "qualifier": null, "schema": "dc"}, {"key": "dc.identifier.urn", "value": "URN:NBN:fi:jyu-201612185147", "language": null, "element": "identifier", "qualifier": "urn", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Pro gradu -tutkielma", "language": "fi", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Master\u2019s thesis", "language": "en", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Matemaattis-luonnontieteellinen tiedekunta", "language": "fi", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Faculty of Sciences", "language": "en", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Matematiikan ja tilastotieteen laitos", "language": "fi", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Department of Mathematics and Statistics", "language": "en", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "University of Jyv\u00e4skyl\u00e4", "language": "en", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "Jyv\u00e4skyl\u00e4n yliopisto", "language": "fi", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Matematiikka", "language": "fi", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Mathematics", "language": "en", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "dc.date.updated", "value": "2016-12-18T19:36:27Z", "language": null, "element": "date", "qualifier": "updated", "schema": "dc"}, {"key": "yvv.contractresearch.funding", "value": "0", "language": null, "element": "contractresearch", "qualifier": "funding", "schema": "yvv"}, {"key": "dc.type.coar", "value": "http://purl.org/coar/resource_type/c_bdcc", "language": null, "element": "type", "qualifier": "coar", "schema": "dc"}, {"key": "dc.rights.accesslevel", "value": "openAccess", "language": "fi", "element": "rights", "qualifier": "accesslevel", "schema": "dc"}, {"key": "dc.type.publication", "value": "masterThesis", "language": null, "element": "type", "qualifier": "publication", "schema": "dc"}, {"key": "dc.subject.oppiainekoodi", "value": "4041", "language": null, "element": "subject", "qualifier": "oppiainekoodi", "schema": "dc"}, {"key": "dc.subject.yso", "value": "diskreetti matematiikka", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.format.content", "value": "fulltext", "language": null, "element": "format", "qualifier": "content", "schema": "dc"}, {"key": "dc.rights.url", "value": "https://rightsstatements.org/page/InC/1.0/", "language": null, "element": "rights", "qualifier": "url", "schema": "dc"}, {"key": "dc.type.okm", "value": "G2", "language": null, "element": "type", "qualifier": "okm", "schema": "dc"}]
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