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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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| Format: | Thesis |
| Language: | English |
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Graduate School of Business (GSB)
2024
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| Summary: | 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.
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