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master's thesis
Modeli lokalne volatilnosti
Zagreb: University of Zagreb, Faculty of Science, 2022. urn:nbn:hr:217:160031
Jelić, Magdalena
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Jelić, M. (2022). Modeli lokalne volatilnosti (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:160031

Jelić, Magdalena. "Modeli lokalne volatilnosti." Master's thesis, University of Zagreb, Faculty of Science, 2022. https://urn.nsk.hr/urn:nbn:hr:217:160031

Jelić, Magdalena. "Modeli lokalne volatilnosti." Master's thesis, University of Zagreb, Faculty of Science, 2022. https://urn.nsk.hr/urn:nbn:hr:217:160031

Jelić, M. (2022). 'Modeli lokalne volatilnosti', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:160031

Jelić M. Modeli lokalne volatilnosti [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2022 [cited 2024 December 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:160031

M. Jelić, "Modeli lokalne volatilnosti", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2022. Available at: https://urn.nsk.hr/urn:nbn:hr:217:160031

Metadata
TitleModeli lokalne volatilnosti
Title (english)Local volatility models
AuthorMagdalena Jelić
MentorVanja Wagner (mentor)
Committee memberVanja Wagner (predsjednik povjerenstva)
Committee memberNenad Antonić (član povjerenstva)
Committee memberDražen Adamović (član povjerenstva)
Committee memberTomislav Pejković (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2022-09-29, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu promatrali smo modele lokalne volatilnosti. Nakon početnog uvođenja potrebnih preliminarija, proučili smo Dupireovu formulu, Derman-Kani formulu te lokalnu volatilnost kao funkciju Black-Scholesove podrazumijevane volatilnosti i opisali izvodenje tih parcijalnih diferencijalnih jednadžbi. Treći dio rada sastoji od samih modela, odnosno prikaza njihovih dinamika. Pomaknuti lognormalni model, kao i model konstantne elastičnosti varijance, postiže kosi smiješak volatilnosti, dok konveksne kombinacije lognormalnih gustoća pružaju bolju aproksimaciju smiješka volatilnosti. Mješoviti lognormalni model s različitim očekivanjima i model mješovitih sinus hiperbolnih gustoća, koje su razvili Brigo i Mercurio, ipak su najbolji medu njima, odnosno zadovoljavaju veći opseg struktura krivulje podrazumijevane volatilnosti.
Abstract (english)
In this thesis, we have observed local volatility models. After introducing needed preliminaries, we have studied Dupire’s formula, formula by Derman and Kani and local volatility as a function of Black-Scholes implied volatility. Moreover, we have described derivation of their partial differential equations. The third part consists of local volatility models and the representation of their dynamics. The shifted lognormal model, as well as the constant elasticity of variance model, achieves only a skewed smile, while lognormal mixtures provide a better approximation of the volatility smile. However, a lognormal-mixture with different means and hyperbolic sine density mixture, developed by Brigo and Mercurio, are the best among these models, that is they accomodate rather general structures of the local volatility curve.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:160031
Study programmeTitle: Finance and Business 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 on2022-10-27 10:20:05