GARCH option pricing models in a South African equity context

Abstract

In this paper, different 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 different GARCH models (one symmetric and two asymmetric) are considered and three different 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 effects outperform competing models in terms of pricing performance.