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master's thesis
Egzotične opcije
2019. urn:nbn:hr:126:044599
Keglević, Nera
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics and Mathematics Teaching
Probability, Mathematical Statistics and Data Science Research Group

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Keglević, N. (2019). Egzotične opcije (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:044599

Keglević, Nera. "Egzotične opcije." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2019. https://urn.nsk.hr/urn:nbn:hr:126:044599

Keglević, Nera. "Egzotične opcije." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2019. https://urn.nsk.hr/urn:nbn:hr:126:044599

Keglević, N. (2019). 'Egzotične opcije', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 15 February 2025, https://urn.nsk.hr/urn:nbn:hr:126:044599

Keglević N. Egzotične opcije [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2019 [cited 2025 February 15] Available at: https://urn.nsk.hr/urn:nbn:hr:126:044599

N. Keglević, "Egzotične opcije", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2019. Available at: https://urn.nsk.hr/urn:nbn:hr:126:044599

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Metadata
TitleEgzotične opcije
Title (english)Exotic Options
AuthorNera Keglević
MentorNenad Šuvak (mentor)
Committee memberMirta Benšić (predsjednik povjerenstva)
Committee memberNenad Šuvak (član povjerenstva)
Committee memberDanijel Grahovac (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Pure Mathematics and Mathematics Teaching)
(Probability, Mathematical Statistics and Data Science Research Group)
Osijek
Defense date and country2019-01-18, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Probability Theory and Statistics
Abstract
Na početku rada predstavljen je model Brownovog gibanja. Za početak, objašnjena je konstrukcija i sama definicija Brownovog gibanja i osnovna svojstva. Nadalje, opisan je model geometrijskog Brownovog gibanja koji je prikladniji za modeliranje cijena dionica. Pokazano je na koji se način mogu simulirati Brownovo gibanje i geometrijsko Brownovo gibanje. Osim toga, predstavljena je Black-Scholes formula za europsku call i put opciju. U drugom su poglavlju navedena svojstva očekivanja i varijance Monte Carlo procjenitelja te kako koristiti Monte Carlo metode prilikom vrednovanja egzotičnih opcija. U trećem su poglavlju objašnjene redom azijska, barrier i lookback opcija te su istaknuta najvažnija svojstva svake pojedine opcije. Naposljetku, simulirane su cijene dionica i promatrani odnosi izmedu cijena europskih call i put opcija i pripadajućih call i put egzotičnih opcija
Abstract (english)
At, its beginning this graduate thesis introduces Brownian motion model. The construction and the definition of Brownian motion are described. Basic properties of Brownian motion are also shown. Furthermore, geometric Brownian motion model is described since it is more suitable for modelling stock prices. Simulations of Brownian and geometric Brownian motion model are demonstrated. Additionally, Black-Scholes formula for European call and put options is introduced. In the second part of paper, expectation and variance of Monte Carlo estimator are formulated and proven, also the benefit of Monte Carlo methods while pricing exotic options is shown. In third part of paper, Asian, barrier and lookback options are explained, furthermore their most important properties are mentioned. Finally, stock prices are simulated, relations between prices of European call and put options and belonging call and put exotic options are observed.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:044599
Study programmeTitle: Mathematics; specializations in: Financial and Statistical Mathematics, Mathematics and Computer Science, Industrial and Applied Mathematics
Course: Financial and Statistical Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2019-01-21 09:13:44