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Levy processes and quantum mechanics : an investigation into the distribution of log returns
Thesis (MCom)--Stellenbosch University, 2021.
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| Format: | Thesis |
| Language: | en_ZA |
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Stellenbosch : Stellenbosch University
2021
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| _version_ | 1867613825981743104 |
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| access_status_str | Open Access |
| author | Le Roux, Christiaan Hugo |
| author2 | De Wet, Tertius |
| author_browse | De Wet, Tertius Le Roux, Christiaan Hugo |
| author_facet | De Wet, Tertius Le Roux, Christiaan Hugo |
| author_sort | Le Roux, Christiaan Hugo |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Thesis (MCom)--Stellenbosch University, 2021. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/109864 |
| institution | Stellenbosch University (South Africa) |
| language | en_ZA |
| last_indexed | 2026-06-10T12:42:17.808Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2021 |
| publishDateRange | 2021 |
| publishDateSort | 2021 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/109864 Levy processes and quantum mechanics : an investigation into the distribution of log returns Le Roux, Christiaan Hugo De Wet, Tertius Stellenbosch University. Faculty of Economic and Management Sciences. Dept. of Statistics and Actuarial Science. Financial Risk Management Log return distribution Distribution (Probability theory) Stock price indexes Economics -- Statistical methods Quantum finance UCTD Thesis (MCom)--Stellenbosch University, 2021. ENGLISH SUMMARY : It is well known that log returns on stocks do not follow a normal distribution as is assumed under the Black-Scholes pricing formula. This study investigates alternatives to Brownian Motion which are better suited to capture the stylized facts of asset returns. Lévy processes and models based on Quantum Mechanical theory are described and t to daily log returns for various JSE Indices. Maximum likelihood estimation is used to estimate the parameters of the Lévy processes and the Cramer-von Mises goodness of t statistic is minimized to estimate the parameters of the Quantum Mechanical models. Q-Q plots and the Kolmogorov-Smirnov t statistic is presented to assess the fit of the various models. The results show that the Lévy processes, specically the Normal Inverse Gaussian process, are the best among the processes considered. The performance of the Quantum Mechanical models could be improved if more eigenstates are considered in the approximation, however the computational expense of these models makes them impractical. AFRIKAANSE OPSOMMING : Dit is bekend dat log opbrengste op aandele nie 'n normale verdeling volg soos in die Black-Scholes prysingsformule aanvaar word nie. Hierdie studie ondersoek alternatiewe tot Brownse Beweging wat beter geskik is om die gestileerde feite van bate opbrengste vas te lê. Lévy prosesse en modelle gebaseer op die kwantummeganiese teorie word beskryf en aangepas tot daaglikse log opbrengste vir verskillende JSE-indekse. Maksimale aanneemlikheid beraming word gebruik om die parameters van die Lévy-prosesse te beraam, en die Cramer-von Mises passingstoets grootheid word geminimeer om die parameters van die kwantummeganiese modelle te beraam. Q-Q stippings en Kolmogorov-Smirnov passingsstatistieke word gebruik om die pasgehalte van die verskillende modelle te evalueer. Die resultate toon dat die Lévy prosesse, spesiek die Normaal Inverse Gaussiese proses, die beste presteer onder die prosesse wat oorweeg word. Die kwantummeganiese modelle kan beter presteer as meer eie state in die benadering gebruik word, maar die berekeningskoste van hierdie modelle maak dit onprakties. Masters 2021-03-01T14:02:56Z 2021-04-21T14:29:22Z 2021-03-01T14:02:56Z 2021-04-21T14:29:22Z 2021-03 Thesis http://hdl.handle.net/10019.1/109864 en_ZA Stellenbosch University xi, 72 pages ; illustrations, includes annexures application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Financial Risk Management Log return distribution Distribution (Probability theory) Stock price indexes Economics -- Statistical methods Quantum finance UCTD Le Roux, Christiaan Hugo Levy processes and quantum mechanics : an investigation into the distribution of log returns |
| title | Levy processes and quantum mechanics : an investigation into the distribution of log returns |
| title_full | Levy processes and quantum mechanics : an investigation into the distribution of log returns |
| title_fullStr | Levy processes and quantum mechanics : an investigation into the distribution of log returns |
| title_full_unstemmed | Levy processes and quantum mechanics : an investigation into the distribution of log returns |
| title_short | Levy processes and quantum mechanics : an investigation into the distribution of log returns |
| title_sort | levy processes and quantum mechanics an investigation into the distribution of log returns |
| topic | Financial Risk Management Log return distribution Distribution (Probability theory) Stock price indexes Economics -- Statistical methods Quantum finance UCTD |
| url | http://hdl.handle.net/10019.1/109864 |
| work_keys_str_mv | AT lerouxchristiaanhugo levyprocessesandquantummechanicsaninvestigationintothedistributionoflogreturns |