magistrsko delo
Andraž Pirnovar (Author), Tomaž Košir (Mentor)

Abstract

Modeliranje verjetnosti neplačila za podjetja je zelo pomembno na področju upravljanja tveganj. V delu je opisana metoda za ocenjevanje te verjetnosti z uporabo trtnih kopul in simulacij lastnega kapitala, ki je predstavljena v Valle_2016. Posebnost te metode je, da temelji na javno dostopnih podatkih iz bilance stanja, saj kot vhodne podatke potrebujemo le kratkoročne in dolgoročne obveznosti ter sredstva. Hkrati se izognemo nekaterim predpostavkam Mertonovega modela, kar omogoča uporabo tudi za srednje velika in manjša podjetja, ki predstavljajo pomemben del slovenskega gospodarstva. Ker so velikokrat poleg verjetnosti neplačila v trenutnem času pomembne tudi verjetnosti v prihodnosti pod določenimi pogoji, smo razširili model z uporabo pogojnih trtnih kopul. To omogoča napovedovanje verjetnosti glede na dodatne parametre, ki jih je možno šokirati za primer stresnih testov. Obe metodi smo uporabili na realnih podatkih podjetja Petrol d.d. za zadnjih deset let, kjer smo pri razširjeni metodi za dodatno spremenljivko uporabili letno spremembo BDP Slovenije. Izkazalo se je, da razširjena metoda deluje kot pričakovano, saj je bil ocenjeni lastni kapital manjši v primeru zmanjšanja BDP. Dodatno smo pokazali, da je za pravilnejšo metodo in boljše delovanje metode pametno uporabiti relativne razlike realnih podatkov v nekem obdobju namesto absolutnih podatkov.

Keywords

kopule;verjetnost neplačila;parne konstrukcije kopul;trtne kopule;Monte Carlo metode;

Data

Language: Slovenian
Year of publishing:
Typology: 2.09 - Master's Thesis
Organization: UL FMF - Faculty of Mathematics and Physics
Publisher: [A. Pirnovar]
UDC: 519.8
COBISS: 27263235 Link will open in a new window
Views: 1041
Downloads: 159
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Other data

Secondary language: English
Secondary title: Modelling default probability with copulas
Secondary abstract: Modelling Probability of default of companies is of the utmost importance in the area of risk management. In this thesis, we describe a method for estimating the probability of default via the usage of vine copulas and the companies' capital simulation, as presented in Valle_2016. The stand out feature of this method is that it uses only balance sheet data, as it needs only short and long term assets and liabilities. Additionally, some of the Merton model assumptions can be discarded, which enables its usage for small and medium enterprises, which comprise a significant part of Slovenia's economy. As forecasting the probability of default under certain conditions is sometimes as important as estimating it in the present, we expanded the model with conditional vine copulas. This expansion enables forecasting with additional parameters, which can be shocked for the usage in stress testing. We used both methods on ten years of real data for the company Petrol d.d. For the expanded method, we used the yearly change of GDP for Slovenia as an additional variable. It turns out that it works as expected, as the simulated own funds were smaller in the case of lowered GDP. Additionally, we have shown that the performance of the method improves, and the method becomes theoretically sounder if we use relative changes of real data over some timeframe instead of absolute valued data.
Secondary keywords: copulas;probability of default;pairwise copula construction;vine copulas;Monte Carlo methods;
Type (COBISS): Master's thesis/paper
Study programme: 0
Embargo end date (OpenAIRE): 1970-01-01
Thesis comment: Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Finančna matematika - 2. stopnja
Pages: IX, 64 str.
ID: 12027605