Određivanje cijene i premošćivanja rizika u slučaju difuzijskog procesa sa skokovima

master's thesis

• Title (english): Option Pricing and Hedging under Jump-diffusion model
• Author: Ivan Almer
• Mentor: Tomislav Burić (mentor)
• Committee member: Tomislav Burić (predsjednik povjerenstva)
• Committee member: Mervan Pašić (član povjerenstva)
• Committee member: Lenka Mihoković (član povjerenstva)
• Granter: University of Zagreb; Faculty of Electrical Engineering and Computing; Zagreb
• Defense date and country: 2022-07-05, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Computing

Abstract

Stohastički procesi imaju široku primjenu u raznim područjima računarske znanosti, a u sklopu ovog rada istražit će se njihova primjena u području financija. Fokus rada je matematički definirati proces cijene nekog sredstva u obliku difuzijskog procesa sa skokovima, na temelju kojeg se naknadno određuje cijena njegovog financijskog derivata. Potrebno je programskim simulacijama cijena sredstva i derivata pokazati njihovo ponašanje u vremenu. Nakon što su spomenuti procesi cijena definirani, želimo pokazati kako se matematički može predstaviti i riješiti problem premošćivanja rizika, te navedeno popratiti programskim simulacijama scenarija s ciljem ilustracije efekta premošćivanja rizika.

Abstract (english)

Stochastic processes have a widespread application in the computer science and in this thesis their application in the field of finance will be studied. The focus of this thesis will be to mathematically define a price of an asset using a jump-diffusion model which is then used to price a derivative. By programming simulations of prices of an asset and its derivative, their behavior in time will be shown. After the prices of an asset and its derivative have been defined, we want to show how to mathematically define a problem of hedging a position. This also has to be accompanied with implemented simulations to illustrate the effect of hedging.

• Keywords: stohastički procesi; financije; određivanje cijene; opcije; premošćivanje rizika
• Keywords (english): stochastic processes; finance; pricing; options; hedging
• Language: english
• URN:NBN: urn:nbn:hr:168:082522
• Study programme: Title: Computing; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra inženjer/inženjerka računarstva (magistar/magistra inženjer/inženjerka računarstva)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Closed access
• Created on: 2023-01-13 11:39:35