Full Text Available
Note: Clicking the button above will open the full text document at the original institutional repository in a new window.
Fourier methods for pricing early-exercise options under levy dynamics
Thesis(MSc)--Stellenbosch University, 2012.
Saved in:
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Thesis |
| Language: | en_ZA |
| Published: |
Stellenbosch : Stellenbosch University
2012
|
| Subjects: | |
| Tags: |
No Tags, Be the first to tag this record!
|
| _version_ | 1867614097485332480 |
|---|---|
| access_status_str | Open Access |
| author | Fadina, Tolulope Rhoda |
| author2 | Ouwehand, P. W. |
| author_browse | Fadina, Tolulope Rhoda Ouwehand, P. W. |
| author_facet | Ouwehand, P. W. Fadina, Tolulope Rhoda |
| author_sort | Fadina, Tolulope Rhoda |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch Univesity |
| description | Thesis(MSc)--Stellenbosch University, 2012. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/71860 |
| institution | Stellenbosch University (South Africa) |
| language | en_ZA |
| last_indexed | 2026-06-10T12:46:37.536Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2012 |
| publishDateRange | 2012 |
| publishDateSort | 2012 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/71860 Fourier methods for pricing early-exercise options under levy dynamics Fadina, Tolulope Rhoda Ouwehand, P. W. Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Options (Finanve) -- Prices Fourier transformations Levy processes Dissertations -- Mathematics Theses -- Mathematics Thesis(MSc)--Stellenbosch University, 2012. ENGLISH ABSTRACT: The pricing of plain vanilla options, including early exercise options, such as Bermudan and American options, forms the basis for the calibration of financial models. As such, it is important to be able to price these options quickly and accurately. Empirical studies suggest that asset dynamics have jump components which can be modelled by exponential Lévy processes. As such models often have characteristic functions available in closed form, it is possible to use Fourier transform methods, and particularly, the Fast Fourier Transform, to price such options efficiently. In this dissertation we investigate and implement four such methods, dubbed the Carr- Madan method, the convolution method, the COS method and the Fourier spacetime stepping method. We begin by pricing European options using these Fourier methods in the Black-Scholes, Variance Gamma and Normal Inverse Gaussian models. Thereafter, we investigate the pricing of Bermudan and American options in the Black-Scholes and Variance Gamma models. Throughout, we compare the four Fourier pricing methods for accuracy and computational efficiency. AFRIKAANSE OPSOMMING: Die prysbepaling van gewone vanilla opsies, insluitende opsies wat vroeg uitgeoefen kan word, soos Bermuda-en Amerikaanse opsies, is grondliggend vir die kalibrering van finansiële modelle. Dit is daarom belangrik dat die pryse van sulke opsies vinnig en akkuraat bepaal kan word. Empiriese studies toon aan dat batebewegings sprongkomponente besit, wat gemodelleer kan word met behulp van exponensiëele Lévyprosesse. Aangesien hierdie modelle dikwels karakteristieke funksies het wat beskikbaar is in geslote vorm, is dit moontlik om Fourier-transform metodes, en in besonders die vinnige Fourier-transform, te gebruik om opsiepryse doeltreffend te bepaal. In hierdie proefskrif ondersoek en implementeer ons vier sulke metodes, genaamd die Carr-Madan metode, die konvolusiemetode, die COS-metode en die Fourier ruimte-tydstap metode. Ons begin deur die pryse van Europese opsies in die Black-Scholes, Gammavariansie (Engels: Variance gamma) en Normaal Invers Gauss (Engels: Normal Inverse Gaussian)-modelle te bepaal met behulp van die vier Fourier-metodes. Daarna ondersoek ons die prysbepaling van Bermuda-en Amerikaanse opsies in die Black-Scholes en Gammavariansiemodelle. Deurlopend vergelyk ons die vier Fourier-metodes vir akkuraatheid en berekeningsdoeltreffendheid. 2012-10-08T09:33:11Z 2012-12-12T08:15:17Z 2012-10-08T09:33:11Z 2012-12-12T08:15:17Z 2012-12 Thesis http://hdl.handle.net/10019.1/71860 en_ZA Stellenbosch Univesity 134 p. : ill. application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Options (Finanve) -- Prices Fourier transformations Levy processes Dissertations -- Mathematics Theses -- Mathematics Fadina, Tolulope Rhoda Fourier methods for pricing early-exercise options under levy dynamics |
| title | Fourier methods for pricing early-exercise options under levy dynamics |
| title_full | Fourier methods for pricing early-exercise options under levy dynamics |
| title_fullStr | Fourier methods for pricing early-exercise options under levy dynamics |
| title_full_unstemmed | Fourier methods for pricing early-exercise options under levy dynamics |
| title_short | Fourier methods for pricing early-exercise options under levy dynamics |
| title_sort | fourier methods for pricing early exercise options under levy dynamics |
| topic | Options (Finanve) -- Prices Fourier transformations Levy processes Dissertations -- Mathematics Theses -- Mathematics |
| url | http://hdl.handle.net/10019.1/71860 |
| work_keys_str_mv | AT fadinatoluloperhoda fouriermethodsforpricingearlyexerciseoptionsunderlevydynamics |