Collateralised option pricing in a South African context : a univariate GARCH approach

Abstract

In this paper, the generalised autoregressive heteroskedasticity (GARCH) model is applied to the pricing of collateralised options in the South African equity market. Symmetric GARCH and nonlinear asymmetric GARCH (AGARCH) models are considered. The models are used to price fully collateralised and zero collateral options (European, Asian, and lookback options). The effect of collateral is illustrated by the difference between zero collateral and fully collateralised option price surfaces. Finally, the effect of asymmetry is shown by the difference between the symmetric and asymmetric GARCH option price surfaces.