20.500.12556/DKUM-77840 Stohastično modeliranje obrestnih mer Stohastic modeling of interest rates Magistrsko delo obravnava napoved obrestnih mer in vpliv gibanja obrestnih mer na anuiteto dolgoročnega kredita. V prvem delu je na kratko povzeta teorija stohastičnih procesov, Brownovega gibanja in Itôvega procesa. Za napoved obrestnih mer so bili uporabljeni Vasickov, CIR in Hull-Whiteov model. V drugem delu so opisane lastnosti modelov ter izpeljava pričakovane vrednosti in variance. V tretjem delu sledi modeliranje 3-mesečnega Euribor-ja. Uporabljena je metoda največje verjetnosti za Vasickov in CIR model, za Hull-Whiteov model pa metoda najmanjšega verjetja. Vključene so napovedi posameznega modela in pregled gibanja naslednjih 20 let. V četrtem delu so analizirani možni načini najema dolgoročnega kredita, predvsem odločitev o fiksni ali spremenljivi obrestni meri. Glede na dobljene rezultate napovedi obrestnih mer je sestavljen amortizacijski načrt in potek dolgoročnega kredita. Delo je zaključeno s poglavjem, kjer so podani odgovori na vprašanje, ali se splača najeti nov kredit in poplačati starega (glede na nizke vrednosti trenutnih obrestnih mer). The thesis discusses the topic of forecasting interest rates and the impact interest rate movements have on long-term loans. The first part briefly summarizes the theory of stochastic processes, Brownian motion and Itô process. Vasicek, CIR and Hull-White models were used to forecast interest rates. The second part presents features of the three models and the derivation of expected value and variance. The third part details the modeling of a 3 month Euribor. For forecasting with Vasicek and CIR models the maximum likelihood estimation method was used, and for Hull-White model the least squares method was used. Forecasts of interest rates and movements for the next 20 years are presented using the three models. The fourth part includes the analysis of possible ways to get a long-term loan, especially with consideration to the choice between getting a fixed or variable rate loan. Based on the forecasting an amortization schedule for a long-term loan was drawn up. The thesis ends with an evaluation whether it is more reasonable to apply for a new loan and pay off the old one (considering currently low interest rates). Stohastični model obrestne mere Vasicek CIR Hull-White napoved kredit amortizacija Stochastic model Vasicek CIR Hull-White prediction loan amortization true true false [I. Štampar] Slovenski jezik Angleški jezik Magistrsko delo/naloga 2020-09-16 13:16:04 2021-01-20 14:05:59 2022-08-09 17:16:23 2021-01-21 03:32:37 2020 0 Maribor 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.856:336.781.5(043.2) 47801859 URN:SI:UM:DK:G8BBSCJ6 MAG_Stampar_Ines_2020.pdf MAG_Stampar_Ines_2020.pdf 1 030938CEA104C343EA9C893E92CFD051 bbe3b52f0483e0bd9408ef64dfae3e187be4ad36b7b59ad34abaf8812f1ac4d0 e15361b4-7c11-11eb-bb7a-00155d0001ca 20.500.12556/dkum/a67e10fc-8b66-4427-a02e-e3d1f3ff0842 https://dk.um.si/Dokument.php?lang=slv&id=146285 Fakulteta za naravoslovje in matematiko 0 0 0