GARCH option pricing models in a South African equity context

Abstract

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

Key words: Econometrics, nancial markets, pricing, stochastic processes.