Stacionarnost GARCH procesa i primjene

master's thesis

• Author: Daniel Stojanović
• Mentor: Siniša Slijepčević (mentor)
• Committee member: Siniša Slijepčević (predsjednik povjerenstva)
• Committee member: Miljenko Marušić (član povjerenstva)
• Committee member: Tina Bosner (član povjerenstva)
• Committee member: Marko Vrdoljak (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2016-07-14, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Glavna tema rada je stacionarnost GARCH procesa. Stacionarnost je bitna kako bi se model mogao koristiti u procjeni budućih vrijednosti vremenskog niza. Zbog povoljnih svojstava GARCH procesa, posebice zbog nekonstantne uvjetne varijance, oni mogu vrlo dobro opisivati vremenske nizove u financijskom svijetu. U kontekstu stacionarnosti općeg GARCH(p,q) procesa, uvodimo i vrlo bitan pojam Ljapunovljevog eksponenta čija će negativnost značiti jaku stacionarnost rješenja jakog GARCH modela. Važno je naglasiti da su ta rješenja također jedinstvena, neanticipativna i ergodska. Također, na kraju se rad bavi i primjenom GARCH modela u upravljanju rizicima trgovine na financijskom tržištu, kroz procjenu VaR-a za burzovne indekse FTSE100 i CROBEX.

Abstract (english)

Main topic of this thesis is strong stationarity of GARCH processes. Stationarity is very important in eventual future values forecasting. Because of its good properties, especially its variable conditional variance, GARCH models are very good at capturing important properties of financial time series. Regarding stationarity of the general GARCH(p,q) case, we also introduce the Lyapunov exponent that plays an integral role in determining the existence of strong stationary solution to GARCH models. We should also note that this solution is unique, nonanticipative and ergodic. In the end, thesis also puts GARCH modeling into use by estimating Value-at-Risk for two stock indices, showing the way GARCH models can be used for risk management.

• Keywords: stacionarnost GARCH procesa; procjena budućih vrijednosti vremenskog niza; vremenski nizovi u financijskom svijetu; Ljapunovljev eksponent; upravljanje rizicima trgovine na financijskom tržištu; burzovni indeks FTSE100; burzovni indeks CROBEX.
• Keywords (english): stationarity of GARCH processes; eventual future values forecasting; financial time series; Lyapunov exponent; risk management; stock index FTSE100; stock index CROBEX.
• Language: croatian
• URN:NBN: urn:nbn:hr:217:337869
• Study programme: Title: Finance and Business Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2019-02-07 13:36:45