Hestonov model stohastičke volatilnosti

master's thesis

• Title (english): Heston's model of stochastic volatility
• Author: Marija Begić
• Mentor: Vanja Wagner (mentor)
• Committee member: Vanja Wagner (predsjednik povjerenstva)
• Committee member: Eduard Marušić-Paloka (član povjerenstva)
• Committee member: Tina Bosner (član povjerenstva)
• Committee member: Mladen Vuković (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2020-12-02, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Hestonov model najpopularniji je model stohastičke volatilnosti za određivanje cijena opcija. Djelomično je za to zaslužna njegova zatvorena forma. Neki autori cijenu call opcije nazivaju poluzatvorenom zbog numeričke integracije koja je potrebna da bismo zadržali P1 i P2. No, Black-Scholesov model takoder zahtjeva numeričku integraciju, kako bi zadržao Φ(d1) i Φ(d2). U tom smislu, Hestonov model daje cijene call opcija koje nisu manje zatvorene od onih u Black-Scholesovom modelu. Razlika je u tome što programski jezici često imaju naviku koristiti standardnu normalnu distribuciju dok Hestonove vjerojatnosti nisu ugniježdene te ih se mora dograditi koristeći numeričku integraciju.

Abstract (english)

Heston model is the most popular model of stochastic volatility for determination option price. The reason for that is its closed form. Some authors may call the price of the call option semi-closed because of the numeric integration that is needed to keep P1 and P2. Black-Scholes model also demands numeric integration to keep Φ (d1) adn Φ (d2). In that sence, Heston model gives prices of call options that are not less closed than the ones in Black-Scholes model. The difference is that programming languages have the habit to use standard normal distribution while Hestons probabilities are not included and we have to include them by using numeric integration.

• Keywords: Hestonov model; model stohastička volatilnost; određivanje cijena opcija
• Keywords (english): Heston model; model of stochastic volatility; determination option price
• Language: croatian
• URN:NBN: urn:nbn:hr:217:183182
• 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: 2021-02-22 12:27:22