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An Investigation into the suitability of using GARCH process for pricing options on the SAFEX all share index futures contracts

This thesis primarily sets out to investigate the possibility of incorporating autoregressive conditional heteroskedasticity (ARCH) assumptions in an option-valuation model for All Share Index option contracts, as an alternative to the constant variance assumption required by the Black-Scholes optio...

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Main Author: Miller, Saul
Other Authors: Dorrington, Robert
Format: Thesis
Language:English
Published: Graduate School of Business (GSB) 2024
Subjects:
Business Science
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access_status_str Open Access
author Miller, Saul
author2 Dorrington, Robert
author_browse Dorrington, Robert
Miller, Saul
author_facet Dorrington, Robert
Miller, Saul
author_sort Miller, Saul
collection Thesis
description This thesis primarily sets out to investigate the possibility of incorporating autoregressive conditional heteroskedasticity (ARCH) assumptions in an option-valuation model for All Share Index option contracts, as an alternative to the constant variance assumption required by the Black-Scholes option-pricing model. This involves an assessment of whether the log-returns of the ALSI futures (the instruments underling the ALSl option) follow an ARCH process. A secondary objective is to assess the potential for using an ARCH process to model the ALST spot log returns. This could have the following uses: • Pricing over-the-counter ALSI spot options. • Using the forecast spot return ARCH volatility as a proxy for the forecast ALSI future log return volatility if they have similarly. This is desirable for pricing options on new futures contracts when there is insufficient historical futures data available to fit an ARCH model. Evidence of ARCH presence is determined by examining autocorrelation in the square error terms of the log returns. Although some statistically significant autocorrelations were found, the lags which exhibited these significant autocorrelations showed no pattern. Furthermore, lags which exhibited these significant autocorrelations changed over time.
format Thesis
id oai:open.uct.ac.za:11427/40529
institution University of Cape Town (South Africa)
language eng
last_indexed 2026-06-10T12:48:49.352Z
license_str Not specified — see source repository
provenance_str_mv Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository
publishDate 2024
publishDateRange 2024
publishDateSort 2024
publisher Graduate School of Business (GSB)
publisherStr Graduate School of Business (GSB)
record_format dspace
source_str UCTD — University of Cape Town Open Access Repository
spelling oai:open.uct.ac.za:11427/40529 An Investigation into the suitability of using GARCH process for pricing options on the SAFEX all share index futures contracts Miller, Saul Dorrington, Robert MacDonald, lain Business Science This thesis primarily sets out to investigate the possibility of incorporating autoregressive conditional heteroskedasticity (ARCH) assumptions in an option-valuation model for All Share Index option contracts, as an alternative to the constant variance assumption required by the Black-Scholes option-pricing model. This involves an assessment of whether the log-returns of the ALSI futures (the instruments underling the ALSl option) follow an ARCH process. A secondary objective is to assess the potential for using an ARCH process to model the ALST spot log returns. This could have the following uses: • Pricing over-the-counter ALSI spot options. • Using the forecast spot return ARCH volatility as a proxy for the forecast ALSI future log return volatility if they have similarly. This is desirable for pricing options on new futures contracts when there is insufficient historical futures data available to fit an ARCH model. Evidence of ARCH presence is determined by examining autocorrelation in the square error terms of the log returns. Although some statistically significant autocorrelations were found, the lags which exhibited these significant autocorrelations showed no pattern. Furthermore, lags which exhibited these significant autocorrelations changed over time. 2024-08-16T13:18:42Z 2024-08-16T13:18:42Z 1999 2024-08-16T11:46:37Z Thesis / Dissertation Masters Masters http://hdl.handle.net/11427/40529 eng application/pdf Graduate School of Business (GSB) Faculty of Commerce
spellingShingle Business Science
Miller, Saul
An Investigation into the suitability of using GARCH process for pricing options on the SAFEX all share index futures contracts
thesis_degree_str Master's
title An Investigation into the suitability of using GARCH process for pricing options on the SAFEX all share index futures contracts
title_full An Investigation into the suitability of using GARCH process for pricing options on the SAFEX all share index futures contracts
title_fullStr An Investigation into the suitability of using GARCH process for pricing options on the SAFEX all share index futures contracts
title_full_unstemmed An Investigation into the suitability of using GARCH process for pricing options on the SAFEX all share index futures contracts
title_short An Investigation into the suitability of using GARCH process for pricing options on the SAFEX all share index futures contracts
title_sort investigation into the suitability of using garch process for pricing options on the safex all share index futures contracts
topic Business Science
url http://hdl.handle.net/11427/40529
work_keys_str_mv AT millersaul aninvestigationintothesuitabilityofusinggarchprocessforpricingoptionsonthesafexallshareindexfuturescontracts
AT millersaul investigationintothesuitabilityofusinggarchprocessforpricingoptionsonthesafexallshareindexfuturescontracts

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