Modeling and Risk Analysis Using Parametric Distributions with an Application in Equity-Linked Securities

Table 4

The estimated parameters of the eight distributions and maximum log-likelihood for the filtered residuals from KOSPI 200’s log return.

Model	No.	Parameters					Log-L.
Cauchy	2	μ	σ				−3517.3
		0.0619	0.5386
Laplace	2	μ	σ				−3255.9
		0.0424	−0.2793
Normal	2	μ	σ				−3268.4
		−0.0040	0.9994
Student’s t	3	μ	σ	ν			−3230.8
		0.0276	0.8475	6.9159
Skew normal	3	μ	σ	α			−3249.3
		−0.0149	0.9967	0.8634
Skew Cauchy	3	μ	σ	α			−3512.6
		0.1782	0.5445	−0.2173
Skew Laplace	3	μ	σ	α			−3249.1
		0.1787	0.371	0.5595
Skew Student’s t	4	μ	σ	α	ν		−3219.3
		0.3423	0.9769	−0.3470	8.0386
Hyperbolic	4	μ	σ	α	β		−3216.3
		0.2849	0.9829	−0.2891	1.7735
NIG	4	μ	σ	α	β		−3217.0
		0.3056	0.9803	−0.3096	2.2403
Variance gamma	4	μ	σ	α	λ		−3215.8
		0.2724	0.9841	−0.2764	2.4234
G. hyperbolic	5	μ	σ	α	β	λ	−3215.8
		0.2725	0.9839	−0.2764	0.1516	2.4171