Računska zahtevnost binomskega modela
delo diplomskega seminarja
Abstract
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.
Keywords
finančna matematika;Gosperjev algoritem;računanje v zaključeni obliki;binomski model;vrednotenje opcij;hipergeometrična zaporedja;
Data
| Language: | Slovenian |
|---|---|
| Year of publishing: | 2021 |
| Typology: | 2.11 - Undergraduate Thesis |
| Organization: | UL EF - Faculty of Economics |
| Publisher: | [B. Pirc] |
| UDC: | 519.8 |
| COBISS: |
79164163
|
| Views: | 723 |
| Downloads: | 45 |
| Average score: | 0 (0 votes) |
| Metadata: |
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Other data
| Secondary language: | English |
|---|---|
| Secondary title: | Computational complexity of the binomial model |
| Secondary 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. |
| Secondary keywords: | Gosper algorithm;closed-form computation;binomial model;option pricing;hypergeometric sequences; |
| Type (COBISS): | Final seminar paper |
| Study programme: | 0 |
| Thesis comment: | Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Finančna matematika - 1. stopnja |
| Pages: | 28 str. |
| ID: | 13595045 |
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