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master's thesis
Mjerenje i upravljanje tržišnim rizikom
Zagreb: University of Zagreb, Faculty of Science, 2024. urn:nbn:hr:217:304573
Domitran, Petar
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Domitran, P. (2024). Mjerenje i upravljanje tržišnim rizikom (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:304573

Domitran, Petar. "Mjerenje i upravljanje tržišnim rizikom." Master's thesis, University of Zagreb, Faculty of Science, 2024. https://urn.nsk.hr/urn:nbn:hr:217:304573

Domitran, Petar. "Mjerenje i upravljanje tržišnim rizikom." Master's thesis, University of Zagreb, Faculty of Science, 2024. https://urn.nsk.hr/urn:nbn:hr:217:304573

Domitran, P. (2024). 'Mjerenje i upravljanje tržišnim rizikom', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:304573

Domitran P. Mjerenje i upravljanje tržišnim rizikom [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2024 [cited 2024 December 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:304573

P. Domitran, "Mjerenje i upravljanje tržišnim rizikom", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2024. Available at: https://urn.nsk.hr/urn:nbn:hr:217:304573

Metadata
TitleMjerenje i upravljanje tržišnim rizikom
Title (english)Measuring and managing market risk
AuthorPetar Domitran
MentorVanja Wagner (mentor)
Committee memberVanja Wagner (predsjednik povjerenstva)
Committee memberNikola Sandrić (član povjerenstva)
Committee memberPavle Goldstein (član povjerenstva)
Committee memberMiljenko Marušić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2024-11-28, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Glavna tema ovog rada je uvid u mjeru tržišnog rizika VaR. U prvom poglavlju dana je definicija VaR-a te su uvedene tri osnovne metode za računanje istog. Također, uz svaku metodu dan je i primjer računanja VaR-a tom metodom na povijesnim podacima. Za kraj poglavlja uveden je i pojam uvjetnog VaR-a (CVaR-a). U drugom poglavlju na VaR gledamo iz Bayesovske perspektive. Poglavlje započinje definicijom aposteriori prediktivne distribucije povrata portfelja te su dane formule za računanje VaR-a i CVaR-a u Bayesovskom okruženju. Poglavlje nastavljamo prezentacijom algoritma za računanje hiperparametara u konjugiranoj apriori distribuciji koji omogućava brzu prilagodbu na promjene volatilnosti. Dodatno, uvedena je i empirijska Bayesovska metoda za računanje hiperparametara. Na kraju su ilustrirane prednosti nove metode testiranjem na simuliranim i empirijskim podacima. U trećem poglavlju nalaze se dokazi pojedinih pomoćnih tvrdnji korištenih u radu.
Abstract (english)
The main topic of this paper is an insight into the market risk measure, VaR. In the first chapter, the definition of VaR is provided, along with an introduction to three fundamental methods for its calculation. Each method is accompanied by an example of calculating VaR using historical data. To conclude the chapter, the concept of Conditional VaR (CVaR) is introduced. In the second chapter, VaR is examined from a Bayesian perspective. The chapter begins with the definition of the posterior predictive distribution of portfolio returns, followed by formulas for calculating VaR and CVaR in a Bayesian framework. The chapter continues with a presentation of an algorithm for specifying hyperparameters in a conjugate prior, which enables quick adaptation to changes in volatility. Additionally, the empirical Bayesian method for calculating hyperparameters is introduced. Finally, the advantages of the new method are illustrated through testing on simulated and empirical data. The third chapter contains proofs of certain auxiliary results used in this thesis.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:304573
Study programmeTitle: Financial and Business Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: sveučilišni magistar matematike (sveučilišni magistar matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2024-11-11 18:02:08