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master's thesis
Vrednovanje opcija na OTC tržištu
Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2019. urn:nbn:hr:126:052247
Rački, Barbara
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics and Mathematics Teaching
Probability, Mathematical Statistics and Data Science Research Group

Institutional repository: Repository of School of Applied Mathematics and Computer Science

Cite this document

Rački, B. (2019). Vrednovanje opcija na OTC tržištu (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:052247

Rački, Barbara. "Vrednovanje opcija na OTC tržištu." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2019. https://urn.nsk.hr/urn:nbn:hr:126:052247

Rački, Barbara. "Vrednovanje opcija na OTC tržištu." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2019. https://urn.nsk.hr/urn:nbn:hr:126:052247

Rački, B. (2019). 'Vrednovanje opcija na OTC tržištu', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 30 July 2024, https://urn.nsk.hr/urn:nbn:hr:126:052247

Rački B. Vrednovanje opcija na OTC tržištu [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2019 [cited 2024 July 30] Available at: https://urn.nsk.hr/urn:nbn:hr:126:052247

B. Rački, "Vrednovanje opcija na OTC tržištu", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2019. Available at: https://urn.nsk.hr/urn:nbn:hr:126:052247

Metadata
TitleVrednovanje opcija na OTC tržištu
Title (english)Pricing of Interestrate Options on OTC Market
AuthorBarbara Rački
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 country2019-10-18, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Probability Theory and Statistics
Abstract
Ideja rada je primjena Black model za vrednovanje opcija na OTC tržištu. Na početku rada predstavljen je model Brownovog gibanja te model geometrijskog Brownovog gibanja koji služi kao osnova za modeliranje cijena vezane imovine. Nadalje, budući da je Black model proširenje Black-Scholes-Mertonovog modela za vrednovanje call i put opcija u nastavku su predstavljene osnovne teorijske pretpostavke Black-Scholes-Mertonovog modela koji nasljeđuje i sam Black model. U radu proširujemo Black model, odnosno predstavljen je model kod kojeg kamatne stope opisujemo slučajnim procesom. Za proširenje Black modela vrlo bitna bit će ekvivalentna martingalna mjera te tržišna cijena rizika, Sharpeov omjer. U četvrtom poglavlju predstavljeno je tržište obveznica i kamatnih stopa te su nakon toga detaljnije analizirane tri najpopularnije opcije na OTC tržištu, cap, floor te swap opcije. Za svaku od opcija analiziran je primjer za koji su podaci preuzeti s bankarskog softvera Bloomberg. Na kraju rada prokomentiran je problem Black modela te su navedena dva generalizirana modela koja se češće koriste u praksi.
Abstract (english)
The main idea of this graduate thesis is to apply the Black model to evaluate interest rate options in the OTC market. At the beginning of thesis, a model of Brown motion is presented, as well as a model of geometric Brown motion which is used as basis for modeling the prices of underlying assets. Furthermore, basic theoretical results about Black-Scholes-Merton model and Black model are presented. We extend Black model by assuming that interest rates are stohastic. The equivalent martingale measure and the market price of the risk (Sharpe ratio) will be very important to extend the Black model. In chapter four we introduced the bond and interest rate markets and then we analyzed the three most popular options on the OTC market, cap, floor and swap options. For each option an example in Bloomberg software is given. At the end of the paper one problem of Black model is discussed and as a solution of that problem two generalized models that are more commonly used in practice are introduced.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:052247
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 on2019-10-25 06:44:17