Monte Carlo methods for pricing American options : delo diplomskega seminarja

Naumovska, Matea (author), Verbič, Miroslav (mentor)

The aim of this thesis is to present different Monte Carlo methods and utilize them to find an estimate of the value of American options. Two methods are presented, each differing in its approach. The distributions of the estimates are identified, and an attempt is made to determine the factors influencing the results. Furthermore, we investigate the impact of variance reduction techniques on these algorithms. The parameters used in these algorithms are based on an example found in the literature. A comparison of the time required for the calculation of the estimate and its precision is made, leading to conclusions drawn from the analysis. This paper lays the foundation for further research into the use of Monte Carlo methods in financial modeling and option pricing. Moreover, whilst this paper primarily focuses on one-dimensional analysis, it sets a solid foundation for future research to explore multidimensional models in option pricing, where it may offer substantial advantages over the deterministic methods.

• Language: English
• Keywords: American option, Monte Carlo, Brownian motion, Tilley method, Longstaff-Schwartz method
• Work type: Bachelor thesis/paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2024
• PID: 20.500.12556/RUL-160399
• UDC: 519.2
• COBISS.SI-ID: 205578755
• Publication date in RUL: 28.08.2024

Secondary language

• Language: Slovenian
• Title: Uporaba Monte Carlo metode za vrednotenje ameriških opcij

Abstract

Cilj tega diplomskega seminarja je predstaviti različne Monte Carlo metode in jih uporabiti za oceno vrednosti ameriških opcij. Predstavljeni sta dve metodi, ki se razlikujeta v pristopu. Določene so porazdelitve ocen, in poskus je narejen za določitev faktorjev, ki vplivajo na rezultate. Poleg tega preučujemo vpliv tehnik zmanjšanja variance na te algoritme. Parametri, uporabljeni v teh algoritmih, temeljijo na primeru iz literature. Narejena je primerjava med časom, potrebnim za izračun ocene, in njihovo natančnostjo, kar vodi do sklepov, izpeljanih iz analize. Ta seminar postavlja temelje za nadaljnje raziskave uporabe Monte Carlo metod v finančnem modeliranju in ceni opcij. Poleg tega, čeprav se ta članek osredotoča predvsem na enodimenzionalno analizo, postavlja trdne temelje za prihodnje raziskave večdimenzionalnih modelov verdnotenja opcij, kjer lahko ponudi znatne prednosti pred determinističnimi metodami.

• Keywords: Ameriška opcija, Monte Carlo, Brownovo gibanje, Tilleyeva metoda, Longstaff-Schwartz metoda