Original title: Optimální opční portfolio v Markowitzově modelu
Translated title: Optimal Option Portfolio in Markowitz Model
Authors: Slimák, Adam ; Večeř, Jan (advisor) ; Kopa, Miloš (referee)
Document type: Bachelor's theses
Year: 2026
Language: slo
Abstract: [eng] [cze]
This thesis deals with the optimization of an option portfolio within the Markowitz framework. We view the price of an asset as a likelihood ratio of state price densities, which allows us to connect classical mean-variance optimization with information theory. By applying a quadratic approximation of the logarithmic utility, we derive the Markowitz optimization problem where the parameters are determined directly from state price densities. We derive the state price densities within the geometric Brownian motion model and numerically optimize portfolios consisting of three and four assets. We show that by including option contracts with optimally chosen strike prices, the investor achieves a higher expected logarithmic return and a better approximation of the physical measure. Táto práca sa zaoberá optimalizáciou opčného portfólia v Markowitzovom modeli. Na cenu aktíva sa pozeráme ako na vierohodný pomer hustôt stavových cien, čo nám umož- ňuje prepojiť klasickú mean-variance optimalizáciu s informačnou teóriou. Kvadratickou aproximáciou logaritmického úžitku odvodíme Markowitzovu úlohu, kde parametre sú určené priamo zo stavových hustôt. Stavové hustoty odvodíme v modeli geometrického Brownovho pohybu a numericky optimalizujeme portfólio zložené z troch a štyroch aktív. Ukážeme, že zahrnutím opčných kontraktov s optimálne zvolenými realizačnými cenami investor dosahuje vyšší očakávaný logaritmický výnos a lepšiu aproximáciu cieľovej miery.
Keywords: European options|portfolio optimization|likelihood approach|hedging|risk neutral measure|mean-variance; Evropské opce|optimalizace portfolia|poměr věrohodnosti|replikace výplaty|neutrální míra rizika|mean-variance

Institution: Charles University Faculties (theses) (web)
Document availability information: Available in the Charles University Digital Repository.
Original record: http://hdl.handle.net/20.500.11956/211305

Permalink: http://www.nusl.cz/ntk/nusl-779075


The record appears in these collections:
Universities and colleges > Public universities > Charles University > Charles University Faculties (theses)
Academic theses (ETDs) > Bachelor's theses