Računska zahtevnost binomskega modela : delo diplomskega seminarja

Pirc, Brina (author), Kokol-Bukovšek, Damjana (mentor), Toman, Aleš (comentor)

Binomski model je model finančnega trga z eno delnico in netveganim bančnim računom, ki se uporablja za vrednotenje delniških opcij. V delu diplomskega seminarja nas je zanimalo, ali formulo za vrednotenje evropskih nakupnih opcij z binomskim modelom lahko zapišemo v zaključeni obliki. To je pomembno, saj zaključena oblika pripomore k učinkovitejšemu računanju. Formula za premijo vsebuje hipergeometrično vrsto. Pri iskanju zaključenih oblik hipergeometričnih vrst smo si pomagali z Gosperjevim algoritmom, katerega glavna značilnost je, da je popoln. To pomeni, da nam bodisi vrne vsoto zapisano v zaključeni obliki bodisi nam pove, da taka oblika ne obstaja. S pomočjo algoritma smo prišli do zaključka, da pri vrednotenju opcij z binomskim modelom zaključena oblika ne obstaja.

• Language: Slovenian
• Keywords: Gosperjev algoritem, računanje v zaključeni obliki, binomski model, vrednotenje opcij, hipergeometrična zaporedja
• Work type: Final seminar paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2021
• PID: 20.500.12556/RUL-131663
• UDC: 519.8
• COBISS.SI-ID: 79164163
• Publication date in RUL: 01.10.2021

PIRC, Brina, 2021, Računska zahtevnost binomskega modela : delo diplomskega seminarja [online]. Bachelor’s thesis. [Accessed 19 April 2025]. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=131663

Secondary language

• Language: English
• Title: Computational complexity of the binomial model

Abstract

The binomial option pricing model is a financial market model with a stock and a risk-free bank account. It is used for the valuation of stock options. The main question of this thesis is whether the plain-vanilla European option pricing formula can be expressed in closed form. This is important because a closed-form solution increases the effectiveness of the calculations. The formula mentioned above contains a hypergeometric series. To find closed-form expressions for hypergeometric series, we use Gosper's algorithm. The key feature of the algorithm is the so-called completeness. This means that it either returns a sum in closed form or tells us that there is no such form. In the end, we conclude that the binomial option pricing formula for plain-vanilla European options has no such closed form.

• Keywords: Gosper's algorithm, closed-form computation, binomial model, option pricing, hypergeometric sequences