Teorija praćenja kreditnog rizika

master's thesis

• Author: Paula Kalajžić
• Mentor: Boris Podobnik (mentor)
• Committee member: Boris Podobnik (predsjednik povjerenstva)
• Committee member: Ivica Nakić (član povjerenstva)
• Committee member: Zvonko Iljazović (član povjerenstva)
• Committee member: Matija Kazalicki (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2015-02-27, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Nakon što smo u prvom poglavlju dobili potrebnu motivaciju za razvoj kvantitativnih metoda proučavanja rizika, u drugom poglavlju upoznajemo jedan od pristupa modeliranju. Osnovni koncepti predstavljeni su kroz primjer modeliranja portfelja dionica te modeliranje portfelja rizičnih kredita. Na koncu se upoznajemo i s dvjema raširenim mjerama rizika - VaR-om te ES-om (expected shortfall-om). Na primjeru modeliranja gubitaka dvjema različitim distribucijama (normalnom i Studentovom t-distribucijom) uočavamo prednosti korištenja expected shortfalla naspram VaR-a. U trećem poglavlju upoznajemo se s tri poznata modela kreditnog rizika. Prvi model koji je razvio Robert C. Merton jedan je od najpoznatijih zbog svog utjecaja na razvoj teorije te kasnije implementacije modela u industriji. Kao primjer jednog takvog industrijskog modela opisan je KMV model. Iako se dijelom nastavlja na Mertonov model, vjerojatnosti defaulta računa koristeći empirijske procjene na temelju velikih baza podataka tvrtki koje su nekada bankrotirale u sličnim uvjetima. Treći model u analizi kreditne sposobnosti koristi kreditne rejtinge od strane priznatih rejting agencija. Pokazali smo da se i takvi modeli mogu uklopiti u formu strukturalnih modela. U zadnjoj sekciji izložen je pristup modeliranju kreditnog rizika portfelja po uzoru na izložene strukturalne modele za jednu tvrtku. Posebice će nas zanimati korelacija defaulta dvaju obveznika te vjerojatnost istovremenog defaulta vise obveznika odjednom. Ključnu ulogu u tome ima pripadna zajednička funkcija distribucije promatranih kritičnih varijabli, čiji pad ispod određene granice označava default. Uvođenjem pojma kopule, razmatraju se razne mogućnosti za izbor zajedničke funkcije distribucije. Na zadnjem primjeru možemo uočiti važnost određivanja što točnije zajedničke funkcije distribucije, budući da pogrešan odabir može dovesti do podcjenjivanja ”težine” desnog repa distribucije gubitaka portfelja.

Abstract (english)

After being provided with motivation for development of quantitative methods of studying risks in the first chapter, the following chapter is devoted to studying one of many possible approaches to risk modelling. We then introduce basic concepts using the examples of stock-portfolio modelling and portfolio credit risk. Finally, two outspreaded risk measures are explained, namely VaR and ES (expected shortfall). Taking the example of loss modelling using two different distributions (normal and Student t-distribution), we note some benefits of using expected shortfall, instead of VaR, as a risk measure. Third chapter is dedicated to three well-known credit risk models. First model, developed by Robert C. Merton, is among the most famous ones due to its influence on the evolution of the theory and its implementation in financial industry. As an example of an industrial model, KMV model is explained more thoroughly. Although it is somewhat an extension of the Merton model, KMV model uses data from big databases of companies which have previously defaulted in similar conditions when estimating a specific probability of default. Third model we examine uses credit ratings obtained from independent agencies in analyzing future credit solvency. Last section of the thesis is devoted to analyzing another approach to modelling a credit risk portfolio- the one based on previously addressed structural models. We are particularly interested in both correlation of defaults of two different counterparties, and the probability of simultaneous defaults of more counterparties. Here the key role is played by joint distribution function of critical variables, whose fall below some preset level symbolizes a default. By introducing copulas, different possibilities of joint distribution function selection are considered. Finally, taking the last exhibited example into consideration, it is possible to acknowledge the importance of choosing as precise joint distribution function as possible, since a less adequate selection can lead to underestimating the weight of the right tail of portfolio loss distribution.

• Keywords: kreditni rizik; modeliranje portfelja dionica; modeliranje portfelja rizičnih kredita; VaR; ES; Mertonov model; KMV model; kreditni rejting
• Keywords (english): credit risk; stock-portfolio modelling; portfolio credit risk; VaR; ES; expected shortfall; Merton model; KMV model; credit rating
• Language: croatian
• URN:NBN: urn:nbn:hr:217:253144
• 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: Access restricted to students and staff of home institution
• Created on: 2019-02-04 10:17:53