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Pricing of options with Lévy processes associated with orthogonal polynomials
Dissertation (MSc)--University of Pretoria, 2018.
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| Format: | Thesis |
| Language: | English |
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University of Pretoria
2019
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| _version_ | 1867613556334133248 |
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| access_status_str | Open Access |
| author2 | Jooste, Alta |
| author_browse | Jooste, Alta |
| author_facet | Jooste, Alta |
| collection | Thesis |
| dc_rights_str_mv | © 2019 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. |
| description | Dissertation (MSc)--University of Pretoria, 2018. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/72649 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:38:00.699Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2019 |
| publishDateRange | 2019 |
| publishDateSort | 2019 |
| publisher | University of Pretoria |
| publisherStr | University of Pretoria |
| record_format | dspace |
| source_str | UPSpace — University of Pretoria Institutional Repository |
| spelling | oai:repository.up.ac.za:2263/72649 Pricing of options with Lévy processes associated with orthogonal polynomials Jooste, Alta u11327465@tuks.co.za Van Zyl, A.J. Chikukwa, Tarutira UCTD Dissertation (MSc)--University of Pretoria, 2018. A Lévy process is a stochastic process that has stationary and independent increments. Log returns of financial assets tend to portray stochastic behaviours possessing distributions with heavy tails, high peaks and negative skewness which justifies the adoption of Lévy processes on modeling these phenomena. In this dissertation we consider two Lévy processes linked to orthogonal polynomials which are the Meixner process and Brownian motion. We build two option pricing models based on these Lévy processes. Both models make use of the Fourier transform methods and their efficiency is judged by the size of the error measures that calculate the distance between the market and model prices. The two models are compared to each other in terms of efficiency, simplicity in application and completeness. We use data from S&P500 index and JSE indices to determine the performances of the models in both liquid (US) and illiquid (SA) markets. Mathematics and Applied Mathematics MSc Unrestricted 2019-12-13T08:07:18Z 2019-12-13T08:07:18Z 19/09/05 2018 Dissertation Chikukwa, T 2018, Pricing of options with Lévy processes associated with orthogonal polynomials, MSc Dissertation, University of Pretoria, Pretoria, viewed yymmdd <http://hdl.handle.net/2263/72649> S2019 http://hdl.handle.net/2263/72649 en © 2019 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. application/pdf University of Pretoria |
| spellingShingle | UCTD Pricing of options with Lévy processes associated with orthogonal polynomials |
| title | Pricing of options with Lévy processes associated with orthogonal polynomials |
| title_full | Pricing of options with Lévy processes associated with orthogonal polynomials |
| title_fullStr | Pricing of options with Lévy processes associated with orthogonal polynomials |
| title_full_unstemmed | Pricing of options with Lévy processes associated with orthogonal polynomials |
| title_short | Pricing of options with Lévy processes associated with orthogonal polynomials |
| title_sort | pricing of options with levy processes associated with orthogonal polynomials |
| topic | UCTD |
| url | http://hdl.handle.net/2263/72649 |