Title Primjena statističkih metoda u kreditnom riziku Title (english) Application of statistical methods in credit risk Author Matko Varga Mentor Nikola Sandrić (mentor)Committee member Nikola Sandrić (predsjednik povjerenstva)Committee member Maja Resman (član povjerenstva)Committee member Boris Širola (član povjerenstva)Committee member Josip Tambača (član povjerenstva)Granter University of Zagreb Defense date and country 2023-03-02, Croatia Scientific / art field, NATURAL SCIENCES Abstract U ovom radu objasnili smo što je kreditni rizik i način na koji su svi sudionici tržišta izloženi kreditnom riziku. Opisali smo zašto je bitno da financijske institucije analiziraju i upravljaju kreditnim rizikom na ispravan način i kako se to odražava na ostvarenje profita. Ključan pojam koji se provlači kroz cijeli diplomski rad jest pojam defaulta, klijentovog neplaćanja. Definirali smo PD, LGD i EAD kao ključne indikatore klijentove rizičnosti. S obzirom da se radi o slučajnim varijablama, uveli smo matematičke modele kojima se može pristupiti procjeni navedenih parametara. U praksi se PD, vjerojatnost ulaska u default, pokazao daleko najbitnijim parametrom, pa je glavni cilj ovog rada bio uvesti model kojim ćemo dobro moći pristupiti procjeni PD-ja. S tim razlogom, definirali smo generalizirani linearni model i objasnili metodu maksimalne vjerodostojnosti. Kao poseban slučaj GLM-a koji dobro može odrediti klijentov PD, naveli smo model logističke regresije. Pretpostavke koje trebaju biti zadovoljene u tom modelu jesu izostanak multi-kolinearnosti među prediktorima, izostanak utjecajnih točaka i linearnost izmedu funkcije veze zavisne varijable i nezavisnih. Demonstrirali smo testiranje značajnosti koeficijenata i interpretaciju rezultata, u terminima šansi, omjera šansi i vjerojatnosti. Posebnu važnost u izboru krajnjeg modela i ocjeni prediktivnosti modela pokazale su veličine poput Akaike informacijskog kriterija i površine ispod ROC krivulje. Krajnje, sva teorija potkrijepljena je primjerom, koristeći bazu o klijentima jedne banke i programski jezik R. Na skupu podataka korištenima u primjeru, kao najznačajnijim varijablama, odnosno onima koje najviše utječu na klijentov ulazak u default, pokazale su se radno iskustvo, debt to income ratio i debt to credit ratio. Dulje radno iskustvo pozitivno je utjecalo na vjerojatnost ulaska u default, odnosno smanjivalo ju je. S druge strane, veći dugovi značili su i veću vjerojatnost defaulta, odnosno rizičnijeg i nepouzdanijeg klijenta.
Abstract (english) In this thesis, it was explained what credit risk is and the means by which all market participants are exposed to it. Successful analysis and management of credit risk proved to be of crucial importance to all financial institutions as it reflects on their profits. Key term that found itself in all the stages of this thesis was default, client’s failure to pay the lender per initial terms. PD, LGD and EAD were defined as main indicators of client’s creditworthiness. Since they are random variables, several mathematical models were introduced as a way to model them. Main goal of this thesis was to establish method of PD assessment, as it proved to be of biggest importance among the three. For that reason, class of generalized linear models was defined and maximum likelihood estimation method explained. Logistic regression was proposed as a special case of GLM which can determine client’s PD particularly well. Assumptions of logistic regression model to be satisfied included absence of multicollinearity among regressors, lack of influential data and linearity between link function of dependent variable and independent ones. Testing for significance of coefficients was demonstrated, as well as interpretation of results, in terms of odds, odds ratio’s and probability. When deciding for a final model and determining its predictive power, values such as Akaike information criterion and area under ROC curve were essential. Lastly, to support the theory, example was given. Database with information on one bank’s clients and programming language R were used. On this data set, variables work experience, debt to income ratio and debt to credit ratio showed to be of biggest influence on client’s de- fault. Longer work experience positively reflected on PD, lowering it. On the other side, bigger debts meant larger PD, making such a client more risky and unrealiable.
Keywords
kreditni rizik
financijske institucije
pojam defaulta
klijentovo neplaćanje
indikatori klijentove rizičnosti
PD
LGD
EAD
model logističke regresije
Keywords (english)
credit risk
financial institutions
PD
LGD
EAD
indicators of client’s creditworthiness
default
client’s failure to pay the lender
Language croatian URN:NBN urn:nbn:hr:217:962502 Study programme Title: Mathematical Statistics Type of resource Text File origin Born digital Access conditions Open access Terms of use Created on 2023-08-24 14:12:36
