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.
