Abstract
In this paper, di erent univariate GARCH option pricing models are applied to the FTSE/JSE Top 40 index to determine the best performing model when modelling the implied South African Volatility Index (SAVI). Three di erent GARCH models (one symmetric and two asymmetric) are considered and three di erent log-likelihood functions are used in the model parameter estimation. Furthermore, the accuracy of each model is tested by comparing the GARCH implied SAVI to the historical SAVI. In addition, the pricing performance of each model is tested by comparing the GARCH implied price to market option prices. The empirical results indicate that the models incorporating asymmetric e ects outperform competing models in terms of pricing performance. Key words: Econometrics, nancial markets, pricing, stochastic processes.
Highlights
In modern finance, asset volatility is synonymous with an asset’s risk
By making use of an approach similar to Hao and Zhang (2013), three different log-likelihood functions are considered for the estimation of the GARCH option pricing model parameters to determine the best performing GARCH model when compared to the historical South African Volatility Index (SAVI)
The log-likelihood function based on the historical SAVI is given by (Hao & Zhang 2013), ln LV
Summary
Asset volatility is synonymous with an asset’s risk. Financial modelling researchers and practitioners face the issue of finding a reliable estimate of volatility. Soczo (2003) explains that historical data can be used to estimate current and future levels of volatility This assumes that the future will be like the past, which is not necessarily a reasonable assumption. GARCH model parameters are usually estimated using historical returns of an asset price, by making use of the maximum likelihood method. Equity volatility indices serve as important financial indicators, measuring the level of risk in markets, while exhibiting predictive power for index returns (see, e.g., Huskaj & Larsson, 2016). By making use of an approach similar to Hao and Zhang (2013), three different log-likelihood functions are considered for the estimation of the GARCH option pricing model parameters to determine the best performing GARCH model when compared to the historical SAVI.
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