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master's thesis
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Semiparametarska procjena VaR-a
Tajana Novak (2017)
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics
Probability and Mathematical Statistics Research Group
Metadata
TitleSemiparametarska procjena VaR-a
AuthorTajana Novak
Mentor(s)Nenad Šuvak (thesis advisor)
Abstract
VaR je mjera rizika koja pruža najbolji omjer dobre teorijske podloge i korisnosti implementacije. Njene slabosti su nedostatak subaditivnosti za neke vrste imovine te činjenica da je samo kvantil distribucije povrata i referira samo minimalni gubitak uz zadanu vjerojatnost. Teorija ekstremnih vrijednosti može se koristiti za modeliranje mjera rizika kao što je value at risk, a primjenjujemo ju na povrate. Takva procjena VaR-a jest semiparametarska. EVT može biti korisna za procjenu veličine ekstremnih događaja, pritom možemo koristiti metodu maksimuma po segmentima ili metodu vrijednosti iznad praga. Metoda vrijednosti iznad praga, koja se oslanja na GPD teorijsku repnu funkciju distribucije, nije se pokazala dobra na promatranim podacima.
KeywordsVaR extreme values theory (EVT) generalised extreme values distribution (GEV) generalized Pareto distribution (GPD) Hill estimator
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
Lower level organizational unitsChair of Pure Mathematics
Probability and Mathematical Statistics Research Group
PlaceOsijek
StateCroatia
Scientific field, discipline, subdisciplineNATURAL SCIENCES
Mathematics
Probability Theory and Statistics
Study programme typeuniversity
Study levelgraduate
Study programmeMathematics; specializations in: Financial and Statistical Mathematics, Mathematics and Computer Science, Industrial and Applied Mathematics
Study specializationFinancial and Statistical Mathematics
Academic title abbreviationmag.math.
Genremaster's thesis
Language Croatian
Defense date2017-10
Parallel abstract (English)
VaR is a risk measure that provides the best ratio of good theoretical background and usefulness of implementation. It’s weaknesses are the lack of subadditivity or some types of assets and the fact that it is only a quantile and refers only to a minimum loss with a given probability. Extreme value theory can be used to model risk measures such as value at risk and we apply it to returns. Such value at risk estimation is semiparametric. EVT can be useful for estimating the size of extreme events, while we can use block maxima or peaks over threshold method. The peaks over threshold method, which relies on fitted GPD tail distribution, didn’t proved to be good on the observed data.
Parallel keywords (Croatian)VaR teorija ekstremnih vrijednosti generalizirana distribucija ekstremnih vrijednosti generalizirana Pareto distribucija Hillov procjenitelj
Resource typetext
Access conditionOpen access
Terms of usehttp://rightsstatements.org/vocab/InC/1.0/
URN:NBNhttps://urn.nsk.hr/urn:nbn:hr:126:494187