Collateralised option pricing in a South African context: A Univariate GARCH approach

Figures & data

Figure 1. Line Graph: Top40 Index Level.

Figure 2. Line Graph: Top40 Returns.

Table 1. Descriptive Statistics: Top40 Returns

	Top40 Returns
Mean	0.0003
Median	1.00E-04
Maximum	0.0468
Minimum	−0.0405
Std. Dev.	0.0102
Skewness	−0.1359
Kurtosis	4.5191
Jarque-Bera	254.4189
Observations	2564

Table 2. GARCH Model Parameters

	GARCH(1,1)	AGARCH(1,1)
$\omega$	2.17E-06*	2.12E-06*
$\alpha$	0.0714*	0.0472*
$\beta$	0.9086*	0.828*
$\lambda$	0.0465*	0.0009
$\gamma$		1.523*
AIC	−6.4385	−6.4866
SIC	−6.4293	−6.4775

* Denotes statistical significance at a 5% level

Figure 3. GARCH(1,1) European call option price surfaces.

Figure 4. European option price differences.

Figure 5. Asian option price differences.

Figure 6. Effect of collateral (lookback option).

Figure 7. Lookback option price differences.