Fourier pricing of two-asset options: a comparison of methods

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dc.contributor.advisorOuwehand, Peteren_ZA
dc.contributor.advisorHuang, Chun-Sungen_ZA
dc.contributor.authorRoberts, Jessica Ellenen_ZA
dc.date.accessioned2018-05-25T07:45:12Z
dc.date.available2018-05-25T07:45:12Z
dc.date.issued2018en_ZA
dc.description.abstractFourier methods form an integral part in the universe of option pricing due to their speed, accuracy and diversity of use. Two types of methods that are extensively used are fast Fourier transform (FFT) methods and the Fourier-cosine series expansion (COS) method. Since its introduction the COS method has been seen to be more efficient in terms of rate of convergence than its FFT counterparts when pricing vanilla options; however limited comparison has been performed for more exotic options and under varying model assumptions. This paper will expand on this research by considering the efficiency of the two methods when applied to spread and worst-of rainbow options under two different models - namely the Black-Scholes model and the Variance Gamma model. In order to conduct this comparison, this paper considers each option under each model and determines the number of terms until the price estimate converges to a certain level of accuracy. Furthermore, it tests the robustness of the pricing methodologies to changes in certain discretionary parameters. It is found that although under the Black-Scholes model the COS method converges in fewer terms than the FFT method for both spread options (32 versus 128 terms) and the rainbow options (64 versus 512 terms), this is not the case under the more complex Variance Gamma model where the terms to convergence of both methods are similar. Both the methodologies are generally robust against changes in the discretionary variables; however, a notable issue appears under the implementation of the FFT methodology to worst-of rainbow options where the choice of the truncated integration region becomes highly influential on the ability of the method to price accurately. In sum, this paper finds that the improved speed of the COS method against the FFT method diminishes with a more complex model - although the extent of this can only be determined by testing for increasingly complex characteristic functions. Overall the COS method can be seen to be preferable from a practical point of view due to its higher level of robustness.en_ZA
dc.identifier.apacitationRoberts, J. E. (2018). <i>Fourier pricing of two-asset options: a comparison of methods</i>. (Thesis). University of Cape Town ,Faculty of Commerce ,Division of Actuarial Science. Retrieved from http://hdl.handle.net/11427/28126en_ZA
dc.identifier.chicagocitationRoberts, Jessica Ellen. <i>"Fourier pricing of two-asset options: a comparison of methods."</i> Thesis., University of Cape Town ,Faculty of Commerce ,Division of Actuarial Science, 2018. http://hdl.handle.net/11427/28126en_ZA
dc.identifier.citationRoberts, J. 2018. Fourier pricing of two-asset options: a comparison of methods. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Roberts, Jessica Ellen AB - Fourier methods form an integral part in the universe of option pricing due to their speed, accuracy and diversity of use. Two types of methods that are extensively used are fast Fourier transform (FFT) methods and the Fourier-cosine series expansion (COS) method. Since its introduction the COS method has been seen to be more efficient in terms of rate of convergence than its FFT counterparts when pricing vanilla options; however limited comparison has been performed for more exotic options and under varying model assumptions. This paper will expand on this research by considering the efficiency of the two methods when applied to spread and worst-of rainbow options under two different models - namely the Black-Scholes model and the Variance Gamma model. In order to conduct this comparison, this paper considers each option under each model and determines the number of terms until the price estimate converges to a certain level of accuracy. Furthermore, it tests the robustness of the pricing methodologies to changes in certain discretionary parameters. It is found that although under the Black-Scholes model the COS method converges in fewer terms than the FFT method for both spread options (32 versus 128 terms) and the rainbow options (64 versus 512 terms), this is not the case under the more complex Variance Gamma model where the terms to convergence of both methods are similar. Both the methodologies are generally robust against changes in the discretionary variables; however, a notable issue appears under the implementation of the FFT methodology to worst-of rainbow options where the choice of the truncated integration region becomes highly influential on the ability of the method to price accurately. In sum, this paper finds that the improved speed of the COS method against the FFT method diminishes with a more complex model - although the extent of this can only be determined by testing for increasingly complex characteristic functions. Overall the COS method can be seen to be preferable from a practical point of view due to its higher level of robustness. DA - 2018 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2018 T1 - Fourier pricing of two-asset options: a comparison of methods TI - Fourier pricing of two-asset options: a comparison of methods UR - http://hdl.handle.net/11427/28126 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/28126
dc.identifier.vancouvercitationRoberts JE. Fourier pricing of two-asset options: a comparison of methods. [Thesis]. University of Cape Town ,Faculty of Commerce ,Division of Actuarial Science, 2018 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/28126en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDivision of Actuarial Scienceen_ZA
dc.publisher.facultyFaculty of Commerceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherMathematical Financeen_ZA
dc.titleFourier pricing of two-asset options: a comparison of methodsen_ZA
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMPhilen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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