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Fourier methods for pricing early-exercise options under levy dynamics

dc.contributor.advisorOuwehand, P. W.en_ZA
dc.contributor.authorFadina, Tolulope Rhodaen_ZA
dc.contributor.otherStellenbosch University. Faculty of Science. Dept. of Mathematical Sciences.en_ZA
dc.date.accessioned2012-10-08T09:33:11Zen_ZA
dc.date.accessioned2012-12-12T08:15:17Z
dc.date.available2012-10-08T09:33:11Zen_ZA
dc.date.available2012-12-12T08:15:17Z
dc.date.issued2012-12en_ZA
dc.identifier.urihttp://hdl.handle.net/10019.1/71860
dc.descriptionThesis(MSc)--Stellenbosch University, 2012.en_ZA
dc.description.abstractENGLISH 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.en_ZA
dc.description.abstractAFRIKAANSE 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.af_ZA
dc.format.extent134 p. : ill.
dc.language.isoen_ZAen_ZA
dc.publisherStellenbosch : Stellenbosch Universityen_ZA
dc.subjectOptions (Finanve) -- Pricesen_ZA
dc.subjectFourier transformationsen_ZA
dc.subjectLevy processesen_ZA
dc.subjectDissertations -- Mathematicsen_ZA
dc.subjectTheses -- Mathematicsen_ZA
dc.titleFourier methods for pricing early-exercise options under levy dynamicsen_ZA
dc.typeThesisen_ZA
dc.rights.holderStellenbosch Univesityen_ZA


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