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Applying stochastic volatility models in the risk-neutral and real-world probability measures
Thesis (PhD (Mathematical Science))--University of Pretoria, 2023.
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University of Pretoria
2023
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| _version_ | 1867613475632578560 |
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| access_status_str | Open Access |
| author2 | Mare, Eben |
| author_browse | Mare, Eben |
| author_facet | Mare, Eben |
| collection | Thesis |
| dc_rights_str_mv | © 2023 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 | Thesis (PhD (Mathematical Science))--University of Pretoria, 2023. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/92276 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:36:44.480Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2023 |
| publishDateRange | 2023 |
| publishDateSort | 2023 |
| 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:2263/92276 Applying stochastic volatility models in the risk-neutral and real-world probability measures Mare, Eben alexilevendis@gmail.com Levendis, Alexis Jacques UCTD Financial engineering Actuarial science Stochastic volatility models Black-Scholes models Simulation SDG-08: Decent work and economic growth SDG-17: Partnerships for the goals Natural and agricultural sciences theses SDG-08 SDG-08: Decent work and economic growth Natural and agricultural sciences theses SDG-17 SDG-17: Partnerships for the goals Thesis (PhD (Mathematical Science))--University of Pretoria, 2023. Stochastic volatility models have become immensely popular since their introduction in 1993 by Heston. This is because their dynamics are more consistent with market behaviour compared to the standard Black-Scholes model. More specifically, stochastic volatility models can somewhat capture the asymmetric distribution often observed in daily equity returns. Numerous extensions to the stochastic volatility model of Heston have since been proposed, including jumps and stochastic interest rates. Due to their complex dynamics, numerical methods such as Monte Carlo simulation, the fast Fourier transform (FFT), and the efficient method of moments (EMM) are often required to calibrate and implement stochastic volatility models. In this thesis, we explore the application of stochastic volatility models to a variety of problems for which research is still in its infancy phase. We consider the pricing of embedded derivatives in the South African life insurance industry given the illiquid derivatives market; the pricing of rainbow and spread options that depend on two underlying assets; the calibration of stochastic volatility models with jumps to historical equity returns; and the use of stochastic volatility models in static hedging. Our findings suggest that stochastic interest rates are the dominant risk driver when pricing long-dated contingent claims; the FFT significantly outperforms Monte Carlo simulation in terms of efficiency; jumps are an important factor required to explain daily equity returns; and static hedging is a simple and effective way to replicate vanilla and exotic options. Insurance and Actuarial Science PhD (Mathematical Science) Unrestricted 2023-09-14T08:48:20Z 2023-09-14T08:48:20Z 2024-04 2023 Thesis Levendis, AJ 2023, Applying stochastic volatility models in the risk-neutral and real-world probability measures, PhD thesis, University of Pretoria, Pretoria. A2024 http://hdl.handle.net/2263/92276 en © 2023 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 Financial engineering Actuarial science Stochastic volatility models Black-Scholes models Simulation SDG-08: Decent work and economic growth SDG-17: Partnerships for the goals Natural and agricultural sciences theses SDG-08 SDG-08: Decent work and economic growth Natural and agricultural sciences theses SDG-17 SDG-17: Partnerships for the goals Applying stochastic volatility models in the risk-neutral and real-world probability measures |
| title | Applying stochastic volatility models in the risk-neutral and real-world probability measures |
| title_full | Applying stochastic volatility models in the risk-neutral and real-world probability measures |
| title_fullStr | Applying stochastic volatility models in the risk-neutral and real-world probability measures |
| title_full_unstemmed | Applying stochastic volatility models in the risk-neutral and real-world probability measures |
| title_short | Applying stochastic volatility models in the risk-neutral and real-world probability measures |
| title_sort | applying stochastic volatility models in the risk neutral and real world probability measures |
| topic | UCTD Financial engineering Actuarial science Stochastic volatility models Black-Scholes models Simulation SDG-08: Decent work and economic growth SDG-17: Partnerships for the goals Natural and agricultural sciences theses SDG-08 SDG-08: Decent work and economic growth Natural and agricultural sciences theses SDG-17 SDG-17: Partnerships for the goals |
| url | http://hdl.handle.net/2263/92276 |