Cox-Ingersoll-Rossov model kamatnih stopa

master's thesis

• Title (english): Cox-Ingersoll-Ross interest rate model
• Author: Matej Oguić
• Mentor: Vanja Wagner (mentor)
• Committee member: Vanja Wagner (predsjednik povjerenstva)
• Committee member: Zrinka Franušić (član povjerenstva)
• Committee member: Nenad Antonić (član povjerenstva)
• Committee member: Tomislav Berić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2022-03-03, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U svome radu iz 1985. J.C.Cox, J.E.Ingersoll i S.A.Ross predlažu generalizaciju Vasičekovog modela, koji opisuje kretanje kamatnih stopa na financijskom tržištu sa samo jednim izvorom rizika. Cox-Ingersoll-Rossov (CIR) model kamatnih stopa tako postaje jedan od najpoznatijih jednofaktorskih vjerojatnosnih modela za modeliranje kamatne stope na financijskom tržištu. U ovom radu je analiziran proces kamatne stope iz CIR modela preko pripadne stohastičke diferencijalne jednadžbe i prikazana su neka svojstva tog procesa, kao što je svojstvo vraćanja prema očekivanju, izvedena je zatvorena forma za uvjetno očekivanje i varijancu te konačno se prezentira izvod cijene i prinosa do dospijeća diskontirane obveznice na financijskom tržištu.

Abstract (english)

J.C.Cox, J.E.Ingersoll, and S.A.Ross, in their work from 1985. propose a generalization of Vasiček’s model, which describes the movement of interest rates in the financial market by only one source of risk. The Cox-Ingersoll-Ross (CIR) interest rate model thus becomes one of the best-known one-factor probability models for modeling interest rates in the financial market. In this thesis, the interest rate process from the CIR model is analyzed through the corresponding stochastic differential equation and some properties of this process are presented, such as the mean reverting property, a closed form for conditional expectation and variance is derived, and finally we obtain the price and yield of discounted bonds in the financial market.

• Keywords: Vasičekov model; Cox-Ingersoll-Rossov (CIR) model kamatnih stopa; financijsko tržište
• Keywords (english): Vasiček’s model; Cox-Ingersoll-Ross (CIR) interest rate model; financial market
• Language: croatian
• URN:NBN: urn:nbn:hr:217:810459
• 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: Open access
• Created on: 2022-06-07 12:16:50